Equation Solver with Steps

Solves an equation and shows each step, from moving terms to the quadratic formula and synthetic division, then checks the roots and draws them. It covers linear, quadratic, cubic, quartic and two simultaneous linear equations.

How to use

1. Type the equation, such as 2(x - 1) = x + 4, with one equation per line for simultaneous equations, or use "Enter coefficients".
2. Check the "Read as" line.
3. Read the "Answer" and "Solution steps". For quadratics pick "Quadratic formula" or "Completing the square"; for systems "Elimination" or "Substitution".
4. Pick "One at a time" and press "Next step" to reveal steps one by one.
5. Press "Similar problem" for a new equation of the same kind.

How it works

• Arithmetic uses exact fractions, so answers appear as fractions, simplified square roots or a ± bi, with decimals beside them.
• Cubics and quartics are factored with the rational root theorem and synthetic division, or the substitution t = x². Roots without an exact form here are found numerically and marked.
• Only polynomial equations are solved: no unknown in a denominator, under a root or inside sin or log.

Questions and answers

How do I solve x² − 5x + 6 = 0?

Two numbers with product 6 and sum −5 are −2 and −3, so (x − 2)(x − 3) = 0 and x = 2 or x = 3.

What is the quadratic formula?

For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a. The sign of b² − 4ac shows two real roots, a double root or two complex roots.

How do I solve a cubic equation step by step?

Test ± (divisors of the constant) ÷ (divisors of the leading coefficient). In x³ − 6x² + 11x − 6 = 0, x = 1 works and synthetic division leaves x² − 5x + 6.

What does it mean when a system has no solution?

The lines are parallel, as x + y = 2 and 2x + 2y = 5 are. If they are the same line, there are infinitely many solutions.