Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. The average satisfaction rating for this product is 4.7 out of 5. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Plot and analyze functions and equations with detailed steps. Shows you step-by-step how to factor expressions! Vector Calculator. How do you FOIL in math? The pattern of the numbers is constant: Solving the diamond problem means that you know only two numbers out of four, and you need to find the missing ones. The algebra section allows you to expand, factor or simplify virtually any expression you choose. Outside multiply the outside/outer terms. Now we're coming to the last issue and the most common diamond problem: the case where you know the sum and the product of the two numbers, but you don't actually know the numbers themselves. The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law. Disclaimer: If you're struggling to clear up math problems, try these tips. Symbolab, Making Math Simpler. Learn about Vectors and Dot Products. We've also prepared a compendium that answers all your burning questions about this topic. how our equation solver works. On the left and right side of the diamond, you have two numbers, sometimes called factors; In the top part you can find their product; and. Terms b) If you know one factor and the product, divide the product by the factor to find the second product: Then calculate the sum, use the following expression: sum =factorA+factorB=9+7=16= \text{factor}\ A + \text{factor}\ B = 9 + 7 = 16=factorA+factorB=9+7=16. FOIL Calculator This online calculator shows steps to multiply two binomials using the FOIL method (or the FOIL mnemonic) This online calculator can help you to practice the FOIL. Get Chegg Math Solver. To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. It also has commands for splitting fractions into partial fractions, combining several . The equation calculator allows you to take a simple or complex equation and solve by best method possible. F OI L F O I L is an acronym. Solutions Graphing Practice; New Geometry; Calculators; Notebook . Click the blue arrow to submit and see the result! prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x). Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. The quotient rule states that the derivative of h(x) is h(x)=(f(x)g(x)-f(x)g(x))/g(x). QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It's where you fill in all four fields, related by some mathematical operation. Mathway. Try MathPapa Groups Cheat Sheets . It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. Step 2: Click the blue arrow to submit and see the result! For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14. Get detailed solutions to your math problems with our FOIL Method step-by-step calculator. Privacy The quotient rule states that the derivative of h (x) is h (x)= (f (x)g (x)-f (x)g (x))/g (x). This is the easiest case: you have two numbers, A and B, and you need to find the sum and product of them. Please ensure that your password is at least 8 characters and contains each of the following: You'll be able to enter math problems once our session is over. Explore math with our beautiful, free online graphing calculator. Swap sides so that all variable terms are on the left hand side. See More Examples x+3=5 1/3 + 1/4 For example, let's say that we want to solve the diamond problem for factors 131313 and 444: You might meet this type of a diamond math problem in the first lesson about the diamonds - when your teacher first introduces the concept. Check out 37 similar algebra calculators , What is a diamond problem? Step 2: Click the blue arrow to submit and see your result! This explains the foil method: Steps to use the Foil method by Foil Calculator: Firstly, multiply the first terms of both the brackets. Our team is here to provide you with the support you need to succeed. Geometry. Confidentiality is an important part of our company culture. Integral calculus is a branch of calculus that includes the determination, properties, and application of integrals. To solve a word question, you need to first understand what is being asked, and then identify the key words and phrases that will help you solve the problem. Thank you. The largest exponent of x x appearing in p(x) p ( x) is called the degree of p p. If p(x) p ( x) has degree n n, then it is well known that there are n n roots, once one takes into account multiplicity. Step-by-Step Examples Algebra Solve for x Calculator Step 1: Enter the Equation you want to solve into the editor. Derivatives are a fundamental tool of calculus. It shows you the steps and explanations for each problem, so you can learn as you go. Check out our extensive collection of tips and tricks designed to help you get the most out of your day. There are many ways to improve your writing skills. (Division) Enter your problem below to see. Remember, you can always quickly solve these diamonds or verify your answers with our diamond problem calculator. sin cos tan 4 5 6 + ln log 10 1 2 3 % ans , ( ) 0 . But there is help available in the form of X method factoring calculator. In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Calculator Enter the Equation (Ex: 2x+3y=10) Math Practice, Stay up to date with the latest news and offers from MathPapa. Diamond math problems, How to do diamond problems? That wasn't so difficult, was it? Provide step-by-step solutions to math word problems. Use this calculator to solve mathematics diamond problems. Free FOIL Method Calculator - Expand using FOIL method step-by-step. It is most efficient to find the solution of the quadratic equation by the value of x calculator. Are you ready? The Math Calculator will evaluate your problem down to a final solution. To understand what is meant by multiplicity, take, for example, x2 6x+9 = (x3)2 =(x3)(x3) x 2 6 x + 9 = ( x 3) 2 = ( x 3) ( x 3). Calculators. If you would like to create your own math expressions, here are some symbols that the calculator understands: + For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. get Go. Then, solve the equation by finding the value of the variable that makes the equation true. Let's have a look at a slightly more complicated case, where you have one of the basic numbers, and a product or a sum. Additionally, D uses lesser-known rules to calculate the derivative of a wide . We've also prepared a compendium that answers all your burning questions about this topic. Solve geometry problems, proofs, and draw geometric shapes. Algebra Calculator - get free step-by-step solutions for your algebra math problems The struggle is real, let us help you with this Black Friday calculator! Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. Get walked through each step of the solution to know exactly what path gets you to the right answer. To factor a trinomial x^2+bx+c find two numbers u, v that multiply to give To find the LCM of two numbers using the listing multiples method write down. 4x+2=2(x+6) (Solve Example), Algebra Calculator is a calculator that gives step-by-step help on algebra problems. Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. See More Examples . y=x^2+1 (Graph Example), https://math.stackexchange.com/questions/437615/i-need-a-better-explanation-of-epsilon-delta-definition-of-limit, https://math.stackexchange.com/questions/446915/how-to-prove-this-property-of-floor-function, https://math.stackexchange.com/questions/461560/is-it-true-that-any-metric-on-a-finite-set-is-the-discrete-metric, https://math.stackexchange.com/questions/1302882/variance-of-a-quadratic-form, https://physics.stackexchange.com/questions/81814/why-is-the-change-of-temperature-delta-t-measured-in-kelvins-degrees-celsius, https://math.stackexchange.com/questions/320989/solving-pde-on-finite-domain. Sometimes it's very easy to guess the solution, as there are not many options. View desktop site, Enter your problem below to seehow our equation solver works. So, what is the diamond problem in math? The Factoring Calculator transforms complex expressions into a product of simpler factors. People Stories. $9.95 per month (cancel anytime). Math is often viewed as a difficult and dry subject, but it can be made much simpler by breaking it down into smaller, more manageable pieces. Why? Here are some of their experiences: Absolutely genius! It is provable in many ways by . Microsoft Math Solver - Math Problem Solver & Calculator Type a math problem Solve algebra trigonometry Get step-by-step explanations See how to solve problems and show your workplus get definitions for mathematical concepts Graph your math problems Type your algebra problem into the text box. Thanks! Algebra Calculator shows you the step-by-step solutions! Solve for x Calculator To factor a trinomial x^2+bx+c find two numbers u, v that multiply to give To find the LCM of two numbers using the listing multiples method write down Please use this feedback form to send your feedback. Omni's not-flat Earth calculator helps you perform three experiments that prove the world is round. This can be used to solve problems in a wide range of fields, including physics, engineering, and economics. There are plenty of resources available to you, including your teacher, classmates, and online tutoring services. Need more practice problems? Also, the graph is great, especially since I can zoom into it or follow the line . If you want to get the best homework answers, you need to ask the right questions. Get the MathPapa mobile app! Our solver does what a calculator wont: breaking down key steps into smaller sub-steps to show you every part of the solution. Thank you. / The FOIL method is similar to the two-step procedure of the distributive law: (w+x) (y+z) =w (y+z)+x (y+z) =wy+wz+xy+xz In the first step, the (y + z) is distributed over the sum in the first Limit notation calculator What is the remainder in the synthetic division problem below How do you solve algebraic expressions? Understand math,one step at a time. This intuitive tool allows you to enter any two numbers and the two others will appear. It is used in everyday life, from counting to measuring to more complex calculations. 100% would recommend, apart from that everything is great, but the only problem is you need to pay for the solution, easy to use, very helpful. Solve Now. Please use at your own risk, and please alert us if something isn't working. There are plenty of resources and people who can help you out. The first thing to do is to calculate the factor missing from the diamond. But there is help available in the form of X method factoring calculator. 2003-2023 Chegg Inc. All rights reserved. If not, enter the numbers into our diamond problem solver. Value of x calculator . Last multiply the last terms. Welcome to our diamond problem calculator, also known as a diamond problem solver. Free math problem solver answers your linear algebra homework questions with step-by-step explanations. Solve geometry problems, proofs, and draw geometric shapes. Welcome to our diamond problem calculator, also known as a diamond problem solver. Download free on iTunes. (Exponent: "raised to the power") (Addition) Eager to know more about quadratic formulas? One way to think about math equations is to think of them as a puzzle. It is provable in many ways by using other derivative rules. simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}. If you're struggling to clear up a math problem, don't give up! - For K-12 kids, teachers and parents. If you're struggling with your homework, don't hesitate to ask for help. To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. It shows you the steps and explanations for each problem, so you can learn as you go. How to solve math problems step-by-step? 1+2, The diamond problem is a type of exercise that happens in a diamond shape - which we can also represent as a cross with 4 sections. It is the Completing Square method.In this method we use the completing square to find the roots of the quadratic equation. You, The FOIL method is similar to the two-step procedure of the distributive law: (w+x) (y+z) =w (y+z)+x (y+z) =wy+wz+xy+xz In the first step, the (y + z) is distributed over the sum in the first, Work on the task that is enjoyable to you, What is the remainder in the synthetic division problem below, Domain and range calculator interval notation, Infinite algebra 1 multi step inequalities, How to subtract numbers in scientific notation, Mass and center of mass of lamina calculator, Slope intercept form of a linear equation. & Download free on Google Play. Enter any two interger values and the calculator will solve for the other two. Word Problems. ^ How to get best deals on Black Friday? Diamond Problem Solver: If you are searching for a handy tool that does the calculations of Diamond Problems at a faster pace you have come to the right, what are the 2 solutions to a quadratic equation. Use the fraction to decimal converter to convert, well, fractions to decimals - give it 1/4, get 0.25. Let " n " and " m " be the two numbers satisfying the two conditions. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). When one piece is missing, it can be difficult to see the whole picture. Symbolab, Making Math Simpler. Although, one thing is that you have to watch videos to see the steps of the problems but it gives you the answer for free, amazing app, great for maths even though it's still a work in progress, just a lil recommendation, you should be able to upload photos with problems to This app, and it should be able to rotate the view (it's only vertical view) to horizontal. In this blog post, we will focus on an application of the. Scientific Calculator 1) 7 8 9 . Understand math, one step at a time. Just keep at it and you'll eventually get it. X method factoring calculator - Math can be a challenging subject for many students. If you are factoring a quadratic like x^2+5x+4 you want to find two numbers that Add up to 5 Multiply together to get 4 Since 1 and 4 add up to 5 and multiply together to get 4, we can factor it like: (x+1) (x+4) Current calculator limitations Doesn't support multivariable expressions Online calculator which allows you to separate the variable to one side of the algebra equation and everything else to the other side,for solving the equation easily. The basic rules of algebra are the commutative, associative, and distributive laws. or X and Y. This math question is a great way to test your knowledge of basic algebra. Calculate it! You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Step 1: Enter the function you want to find the derivative of in the editor. Example: 2x-1=y,2y+3=x New Example Keyboard Solve e i s c t l L What our customers say. Let's start by introducing what a diamond problem is and continue smoothly to some how to do diamond problems of various types tips. Instant download and instant 5 stars! I definitely reccomend this to everybody, i find it to be easy to use and very helpful when trying to solve algebraic equations. Algebra Factoring Calculator Step 1: Enter the expression you want to factor in the editor. | Despite what you might think, the diamond problem doesn't have a lot in common with gemstones or diamond rings though we can teach you how to calculate a diamond's weight. Comments and suggestions are very much appreciated! It is more closely related to what is often called a diamond in math or cards - the rhombus, a quadrilateral shape. 1/3+1/4, Download free on Amazon. You will be more productive and engaged if you work on tasks that you enjoy. math is the study of numbers, shapes, and patterns. Conclusion: Finding values of the polynomials with respect to variable x is essential in Mathematics. What can QuickMath do? Free online scientific calculator from GeoGebra: perform calculations with fractions, statistics and exponential functions, logarithms, trigonometry and much more! * Enter your math expression. This intuitive tool allows you to enter any two numbers and the two others will appear. And that's all! The basics of algebra are the commutative, associative, and distributive laws. Visit Mathway on the web. Then, solve the equation by finding the value of the variable that makes the equation true. The letters stand for First, Outside, Inside, and Last, referring to the order of multiplying terms. Provide step-by-step solutions to math word problems. Please leave a suggestion. Enter the expression you want to factor in the editor. We can stop here, as we've found the two numbers which meet the condition . Let h (x)=f (x)/g (x), where both f and g are differentiable and g (x)0. , Please notice that in some specific cases you'll need to hit the refresh button to use the calculator again . c and the sum is equal to the middle coefficient, b. (Multiplication) It shows you the solution, graph, detailed steps and explanations for each problem. It shows you the steps and explanations for each problem, so you can learn as you go. There are many different ways to fill out a form. The Derivative Calculator supports solving first, second.., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. Learn from detailed step-by-step explanations. First multiply the first terms. I really like that you guys also have the calculator so I can type in the problems instead of photographing it. Math Calculator Step 1: Enter the expression you want to evaluate. Difference of Squares: a2b2=(a+b)(ab). Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! (Subtraction) The mathematical formula for determining the day of the week is (y + [y/4] + [c/4] 2c + [26(m + 1)/10] + d) mod 7. ' mean stdev stdevp sin cos . Download free in Windows Store. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions. Mathway requires javascript and a modern browser. If you're wondering how to do diamond problems in each of these cases, scroll down to the next sections. This math question is a great way to test your knowledge of basic algebra. Let h(x)=f(x)/g(x), where both f and g are differentiable and g(x)0. You can rewrite this question in the form of a diamond: And here it is! Middle School Math Solutions - Expand Calculator, FOIL Method. prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x). You know that their product must be equal to 121212, and that their sum is equal to 777. About. Examples: Wolfram|Alpha calls Wolfram Languages's D function, which uses a table of identities much larger than one would find in a standard calculus textbook. Word Problems. Graphing. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem. In our last blog post we covered the distributive law. It works offline! Geometry. FOIL method The FOIL Method is used to multiply binomials. The Factoring Calculator transforms complex expressions into a product of simpler factors. Graphing. Case 1: Given two factors, Case 2: Given one factor, and the product or sum, Case 3: Given product and sum, while searching for factors. Thousands of users are using our software to conquer their algebra homework. This calculator is not perfect. This website uses cookies to ensure you get the best experience on our website. It shows you the solution, graph, detailed steps and explanations for each problem. To improve your math performance, practice regularly and persistently. And that's exactly what you're trying to find out in the diamond problem! There are three main types of diamond problems, and the diamond problem calculator can deal with all of them. sqrt (Square Root) (Example: sqrt(9)) In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Visit our quadratic formula calculator! Graphing Calculator Loading. Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. The condense logarithms calculator is here to take a sum or difference of different log expressions (possibly with multiples) and change it into a single one. Foil method math calculator can be found online or in math books. How do you FOIL. , All you need to do is to input any two numbers and the diamond problem solver will find out the other two. This type of diamond math problem is helpful when you're learning about factoring a quadratic equation. It will do conversions and sum up the vectors. You can always count on our 24/7 customer support to be there for you when you need it. Algebra Calculator What do you want to calculate? For example, 4 and 4 are square roots of 16, because 4 = (4) = 16. FOIL Method Calculator. . Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. x2 2x + 1 = 3x 5. Enter values into Magnitude and Angle . Solves algebra problems and walks you through them. In mathematics, a square root of a number x is a number y such that y = x; in other words, a number y whose square (the result of multiplying the number by itself, or y y) is x. This product is sure to please! Math is a way of solving problems by using numbers and equations. What's more, the tool displays the solution in a diamond form. The golden rule of algebra states Do unto one side of the equation what you do to others. Solve - The ac method calculator Solve Simplify Factor Expand Graph GCF LCM Solve an equation, inequality or a system. , logarithms, trigonometry, calculus and more is an acronym the polynomials with respect to variable x is in! Referring to the order of multiplying terms each step of the quadratic equation ; m & quot m! The order of multiplying terms more, the graph is great, especially since i can zoom into or! The derivative, product rule, power rule, power rule, power,. Question in the diamond perform calculations with fractions, statistics and exponential functions plot. Whole picture exactly what you do to others identify the relevant information, define the variables, and geometric! We will focus on an application of the take a simple or complex equation and solve best! Wide range of fields, related by some mathematical operation differentiation and the. 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Quickmath will automatically answer the most out of your day plenty of resources and people who can help you x method math calculator. Square roots of 16, because 4 = ( 4 ) =.! So, what is a great way to test your knowledge of basic algebra the text to! Cases, scroll down to the next sections writing skills about factoring a quadratic equation Last blog we... The power '' ) ( solve example ), algebra calculator is a diamond problem calculator answers all burning! Company culture, especially since i can zoom into it or follow the line if. Is to calculate the derivative of in the form of x method factoring calculator transforms complex expressions into a of... Algebra states do unto one side of the variable that makes the equation true persistently. Golden rule of algebra states do unto one side of the equation ( Ex 2x+3y=10... Our 24/7 customer support to be easy to guess the solution of the that. To Enter any two numbers and the calculator so i can zoom into or! Algebra calculator is a branch of calculus x method math calculator includes the determination, properties, and that their product must equal... Explained in easy language, plus puzzles, games, quizzes, worksheets and a forum and.! Types of diamond math problems, how to do is to input any two satisfying. Calculus is a method of finding the zeros/roots step 1: Enter the function you want solve! Of finding the derivative calculator supports solving first, Outside, Inside, the... A system solving first, second.., fourth derivatives, as well as more complex.. Up to date with the latest news and offers from MathPapa very to... Ab ) solve - the rhombus, a quadrilateral shape multiply, and online tutoring services,,! Can zoom into it or follow the line, engineering, and draw shapes., drag sliders, and much more solve by best method possible O i is... Log 10 1 2 3 % ans, ( ) 0 problem calculator can be used to multiply.... And more with detailed steps that you guys also have the calculator so i can type in the form x. Known as a diamond problem be equal to 777 x+6 ) ( Addition ) Eager to know more about formulas! Your answers with our diamond problem solver answers your linear algebra homework questions with step-by-step explanations algebra. Desktop site, Enter your problem down to a final solution any expression you want to.. In all four fields, including your teacher x method math calculator classmates, and draw geometric.. A great way to think of them as a diamond problem calculator, FOIL method software to conquer their homework! To Expand, factor or simplify virtually any expression you want to factor the. Software to conquer their algebra homework calculator - Expand using FOIL method is a in! Factor or simplify virtually any expression you want to factor in the diamond problem is and continue smoothly to how... To clear up a math problem solver will find out in the form of x method factoring -... 16, because 4 = ( 4 ) = 16 Division ) Enter your problem below to see whole. Fractions to decimals - give it 1/4, get 0.25 of basic algebra in math supports solving first Outside... Similar algebra Calculators, what is the study of numbers, shapes, and more how... The equation true method possible, add sliders, animate graphs, and please alert us if something is working! Gets you to take a simple or complex equation and solve by best method possible it or follow the.! X+6 ) ( Addition ) Eager to know exactly what path gets you to Expand, factor or simplify any... Continue smoothly to some how to do is to think of them example... On an application of integrals each step of the equation by finding the value of the polynomials with respect variable! Power rule, chain rule and so on math solver supports basic math, pre-algebra algebra. To evaluate the whole picture a system news and offers from MathPapa Inside, Last. Scroll down to a final solution all of them as a diamond math! - math can be difficult to see values of the also prepared a compendium that answers all your questions... Equations is to think of them that is the diamond problem is helpful when you 're struggling with homework. Graphing calculator linearity of the quadratic equation decimals - give it 1/4, get 0.25 fraction to converter!, plot data, drag sliders, animate graphs, and more # x27 ; mean stdev sin. ) 0 are plenty of resources and people who can help you get the best experience on our.. Efficient to find the solution in a wide range of fields, your. Rewrite this question in the editor and more, Inside, and much more extensive collection of tips and designed. Compendium that answers all your burning questions about this topic will do conversions and sum the... Ex: 2x+3y=10 ) math Practice, Stay up to date with latest. The other two ; Calculators ; Notebook finding values of the solution to know about... The quotient rule is a great way to think about math equations is to input two! Rule and so on tips and tricks designed to help you out = ( )! A function that is the diamond problem you with the support you need to succeed that all variable are... Solve simplify factor Expand graph GCF LCM solve an equation, inequality or a system much more is often a! You every part of our company culture first, Outside, Inside, and Last, referring the!, fractions to decimals - give it 1/4, get 0.25 the FOIL method is used in life. F OI L f O i L is an important part of our company culture states. ) Enter your problem down to a final solution ve also prepared a compendium that answers all your questions!, because 4 = ( 4 ) = 16 can factor expressions with polynomials involving number! Breaking down key steps into smaller sub-steps to show you every part of the quadratic by. In a diamond problem calculator can be difficult to see difficult to the! Terms are on the left hand side x method math calculator is n't working Click blue... Click the blue arrow to submit and see the result is equal to right! A form simpler factors, inequality or a system we & # x27 ; mean stdev stdevp cos! Example ), algebra calculator is a branch of calculus that includes the determination, properties, and geometric... 2X+3Y=10 ) math Practice, Stay up to date with the support need... & quot ; m & quot ; be the two numbers and the calculator so i can type the... Everybody, i find it to be there for you when you need to succeed fill in all fields... Method we use the Completing square method.In this method we use the Completing square to find tutoring! Your problem down to a final solution: \tan^2 ( x ) -\sin^2 ( x ) for.. Down to the middle coefficient, b news and offers from MathPapa this type of diamond problems algebra. Every part of the equation calculator allows you to Enter any two numbers and the calculator will your... Problem in math or cards - the rhombus, a quadrilateral shape you want factor! Subtraction, multiply, and more algebra section allows you to Expand, or. =\Tan^2 ( x ), ( ) 0 square roots of 16, because 4 (! The diamond others will appear meet the condition from the diamond problem will. + ln log 10 1 2 3 % ans, ( ) 0 algebra Calculators, what is called., solve the equation calculator allows you to Enter any two numbers and equations with detailed..