Algebra • Step-by-Step

Solve x² - 9 = 0 with Steps

Solve x² - 9 = 0 step by step using factoring (x - 3)(x + 3) = 0 and square roots x = ±3 with complete working.

Problem Statement

x^2 - 9 = 0

Final Result

x_1 = -3, \quad x_2 = 3

Formula Required: Difference of Two Squares

Take square roots of both sides or factor into (x - 3)(x + 3) = 0.

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

6 Steps

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

x^2 - 9 = 0

Find two numbers that multiply to $c = -9$ and add up to $b = 0$.

(3) \times (-3) = -9, \quad (3) + (-3) = 0

Write the quadratic expression in factored form.

(x + 3)(x - 3) = 0

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

x + 3 = 0 \implies x_1 = -3 \quad \text{or} \quad x - 3 = 0 \implies x_2 = 3

Verify each root by substituting back into the original equation.

\text{Check } x = -3: \; (-3)^2 - 9 = 9 + 0 - 9 = 0 \;\checkmark \\[6pt] \text{Check } x = 3: \; (3)^2 - 9 = 9 + 0 - 9 = 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} = -9

Interactive Calculator

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

The roots are x = 3 and x = -3.