Algebra • Step-by-Step

Solve x² - 16 = 0 with Steps

Step-by-step solution for x² - 16 = 0. Factor into (x - 4)(x + 4) = 0 or take square roots to get x = ±4.

Problem Statement

x^2 - 16 = 0

Final Result

x_1 = -4, \quad x_2 = 4

Formula Required: Difference of Squares

x² = 16 ⇒ x = ±4.

x^2 - 16 = (x - 4)(x + 4) = 0

6 Steps

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

x^2 - 16 = 0

Find two numbers that multiply to $c = -16$ and add up to $b = 0$.

(4) \times (-4) = -16, \quad (4) + (-4) = 0

Write the quadratic expression in factored form.

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

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

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

Verify each root by substituting back into the original equation.

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

Interactive Calculator

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

x = 4 and x = -4.