Solve For X Calculator — Step-by-Step Solutions

The Solve For X Calculator finds the value of x in algebraic equations. It handles linear equations, quadratic equations, and many polynomial equations, providing all solutions including complex roots where applicable.

Enter your equation (e.g. 2x + 5 = 15 or x^2 - 4 = 0) and the calculator will solve for x, showing all possible solutions.

f(x) = 0 (enter f(x))

Solution

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Your calculations will appear here

How to Use the Solve For X Calculator

Enter an equation with x (e.g. 2x + 5 = 15 or x^2 - 9 = 0).
The calculator finds all solutions for x, including complex roots.
It uses Newton's method with multiple starting points to find all roots.

Formula and Theory

Solving an equation means finding all values of the variable that make the equation true. Linear equations (ax + b = 0) have one solution. Quadratic equations have up to two solutions. Higher-degree polynomials can have more.

Newton's method is a numerical approach that iteratively improves an estimate of the root. Starting from an initial guess x0, it computes x1 = x0 - f(x0)/f'(x0) until convergence.

Worked Examples

Example 1: Linear equation

Problem: Solve 3x + 7 = 22

Solution: 3x = 22 - 7 = 15. x = 15/3

Answer: x = 5

Example 2: Quadratic equation

Problem: Solve x^2 - 9 = 0

Solution: x^2 = 9. x = +/- sqrt(9)

Answer: x = 3 or x = -3

Frequently Asked Questions

What types of equations can this solve?

It handles linear, quadratic, polynomial, and many transcendental equations. Some complex equations may not find all roots numerically.

Why does it sometimes miss solutions?

Newton's method depends on starting points. The calculator uses 21 different starting points to maximise coverage, but very unusual functions may have roots that are missed.