Math

Algebra Calculator

Solve linear and quadratic equations with step-by-step solutions.

Linear Equation

ax + b = c

?x + ? = ?

Try:

Quadratic Equation

ax²+bx+c=0

?x² + ?x + ? = 0

Try:

Quadratic Formula

x = (−b ± √(b²−4ac)) / 2a

Δ > 0

Two distinct real roots

Δ = 0

One repeated real root

Δ < 0

Two complex conjugate roots

Vieta's Formulas

For ax² + bx + c = 0 with roots x₁, x₂:

Sum of rootsx₁ + x₂ = −b / a
Product of rootsx₁ × x₂ = c / a
Factored forma(x − x₁)(x − x₂) = 0

Algebraic Identities

(a+b)²= a² + 2ab + b²
(a−b)²= a² − 2ab + b²
(a+b)(a−b)= a² − b²
(a+b)³= a³ + 3a²b + 3ab² + b³
(a−b)³= a³ − 3a²b + 3ab² − b³

Completing the Square

Alternative method for ax² + bx + c = 0:

1. x² + (b/a)x = −c/a

2. add (b/2a)² to both sides

3. (x + b/2a)² = (b²−4ac) / 4a²

4. x = −b/2a ± √(b²−4ac) / 2a