Algebra • Step-by-Step

Solve x² - 8x + 16 = 0 with Steps

Find the repeated root of x² - 8x + 16 = 0 step by step. Shows perfect square factoring (x - 4)² = 0 with discriminant Δ = 0 to yield x = 4.

Problem Statement

x^2 - 8x + 16 = 0

Final Result

x = 4

Formula Required: Perfect Square (x - k)²

Discriminant: (-8)² - 4(1)(16) = 64 - 64 = 0.

(x - 4)^2 = 0 \implies x = 4

6 Steps

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

x^2 - 8x + 16 = 0

Find two numbers that multiply to $c = 16$ and add up to $b = -8$.

(-4) \times (-4) = 16, \quad (-4) + (-4) = -8

Write the quadratic expression in factored form (perfect square trinomial).

(x - 4)^2 = 0

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

x - 4 = 0 \implies x = 4

Verify the solution by substituting back into the original equation.

\text{Check } x = 4: \; (4)^2 - 8(4) + 16 = 16 - 32 + 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} = 8, \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 (multiplicity 2).