# What is the answer to a math problem?

Evaluates, simplifies, solves, differentiates, integrates.

- Page: https://www.acalculator.org/math/math-calculator
- JSON spec: https://www.acalculator.org/math/math-calculator.json
- Version: d00ec35cd8f3

## Default answer

Example with the default inputs (Math problem (3/4 + 1/6) * 12 + sqrt(50), What to do Evaluate): The value of (3/4 + 1/6) * 12 + sqrt(50) is 18.07106781.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| q | Math problem | Numbers, or an expression or equation in one letter. |
| mode | What to do | What to do with the problem. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| value | Value | The value. |
| simplified | Simplified | A simpler equal form. |
| solutions | Solutions | Every real solution. |
| derivative | Derivative | The derivative. |
| antiderivative | Integral | An antiderivative. |

## Method

A computer algebra system; each answer is checked numerically.

## Assumptions

- Real numbers only; angles in radians.

## Worked examples

1. q = (3/4 + 1/6) * 12 + sqrt(50), mode = evaluate gives value = 18.071068.
2. q = 2x + 7 = 19, mode = solve gives solutions = x = 6. Source: OpenStax College Algebra 2e, 2.2, Ex. 1. https://openstax.org/books/college-algebra-2e/pages/2-2-linear-equations-in-one-variable.

## FAQ

### What can this math calculator do?

Five things from one box. Evaluate gives the value of a number expression such as (3/4 + 1/6) × 12 + √50, as a decimal. Simplify rewrites an expression such as (x² − 9)/(x² + 4x + 3). Solve finds every real solution of an equation such as 2x + 7 = 19. Derivative and Integral do the calculus. Each has its own page too, with more options: the simplify calculator, the equation solver, the derivative calculator and the integral calculator.

### How do I type powers, roots and fractions?

Use ^ for a power (x^2), sqrt(…) for a square root, cbrt(…) for a cube root, and / for a fraction, with brackets around a numerator or denominator that has more than one term: (x + 1)/(x - 1). pi is π and e is Euler’s number. A number next to a letter or a bracket multiplies: 2x, 3(x + 1).

### Why does Evaluate say it works on numbers only?

Evaluate gives one number, so every part must be a number. With a letter in the expression, choose Simplify, Solve, Derivative or Integral, or put a number in place of the letter.

### Why does the value have 10 significant figures?

Decimals are shown to 10 significant figures, which is more than enough for homework and most practical work. For an exact form with roots and fractions kept, such as 11 + 5 sqrt(2), use Simplify. Very large numbers, past about 9 × 10¹⁵, are rounded in the last digits.

### Is it a replacement for showing my work?

No. It shows the answer, not the steps, and it is meant for checking your own work. The other pages explain the methods, with worked examples from OpenStax textbooks.

### What does "No verified answer" mean?

Every answer is compared with what you typed, using numbers, before it is shown. If the check fails, if the algebra finds no formula, or if the work takes over 3 seconds, the page says "No verified answer" instead of showing something it could not check.

## Sources

- OpenStax, College Algebra 2e, section 2.2 Linear Equations in One Variable: https://openstax.org/books/college-algebra-2e/pages/2-2-linear-equations-in-one-variable
- OpenStax, College Algebra 2e, section 1.6 Rational Expressions: https://openstax.org/books/college-algebra-2e/pages/1-6-rational-expressions
- OpenStax, Calculus Volume 1, section 3.3 Differentiation Rules: https://openstax.org/books/calculus-volume-1/pages/3-3-differentiation-rules
- OpenStax, Calculus Volume 1, section 4.10 Antiderivatives: https://openstax.org/books/calculus-volume-1/pages/4-10-antiderivatives