Algebra • Step-by-Step

Solve x² - 2x - 8 = 0 with Steps

Solve x² - 2x - 8 = 0 step by step. Factor into (x - 4)(x + 2) = 0 to find solutions x = 4 and x = -2 with complete working.

Problem Statement

x^2 - 2x - 8 = 0

Final Result

x_1 = -2, \quad x_2 = 4

Formula Required: Quadratic Formula & Factoring

Discriminant: 4 + 32 = 36. Square root of 36 is 6.

x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-8)}}{2(1)}

6 Steps

Write the equation in standard quadratic form $ax^2 + bx + c = 0$.

x^2 - 2x - 8 = 0

Find two numbers that multiply to $c = -8$ and add up to $b = -2$.

(2) \times (-4) = -8, \quad (2) + (-4) = -2

Write the quadratic expression in factored form.

(x + 2)(x - 4) = 0

Set each factor equal to zero and solve for $x$.

x + 2 = 0 \implies x_1 = -2 \quad \text{or} \quad x - 4 = 0 \implies x_2 = 4

Verify each root by substituting back into the original equation.

\text{Check } x = -2: \; (-2)^2 - 2(-2) - 8 = 4 + 4 - 8 = 0 \;\checkmark \\[6pt] \text{Check } x = 4: \; (4)^2 - 2(4) - 8 = 16 - 8 - 8 = 0 \;\checkmark

Structural Insight (Vieta's Formulas): Notice how the sum and product of the roots directly confirm the original coefficients.

\text{Sum of roots: } x_1 + x_2 = -\frac{b}{a} = 2, \quad \text{Product: } x_1 \cdot x_2 = \frac{c}{a} = -8

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

x = 4 and x = -2.