Algebra • Step-by-Step

Solve x² - 4 = 0 with Steps

Find the roots of x² - 4 = 0 step-by-step using difference of squares (x - 2)(x + 2) = 0 and square roots x = ±2.

Problem Statement

x^2 - 4 = 0

Final Result

x_1 = -2, \quad x_2 = 2

Formula Required: Difference of Squares Identity

Rewrite as x² - 2² = (x - 2)(x + 2) = 0.

a^2 - b^2 = (a - b)(a + b) = 0

6 Steps

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

x^2 - 4 = 0

Find two numbers that multiply to $c = -4$ and add up to $b = 0$.

(2) \times (-2) = -4, \quad (2) + (-2) = 0

Write the quadratic expression in factored form.

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

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

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

Verify each root by substituting back into the original equation.

\text{Check } x = -2: \; (-2)^2 - 4 = 4 + 0 - 4 = 0 \;\checkmark \\[6pt] \text{Check } x = 2: \; (2)^2 - 4 = 4 + 0 - 4 = 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} = 0, \quad \text{Product: } x_1 \cdot x_2 = \frac{c}{a} = -4

Interactive Calculator

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

x = 2 and x = -2 (or x = ±2).