Algebra • Step-by-Step

Solve x² - 6x + 8 = 0 with Steps

Find the roots of x² - 6x + 8 = 0 step by step. Factor into (x - 2)(x - 4) = 0 to get x = 2 and x = 4.

Problem Statement

x^2 - 6x + 8 = 0

Final Result

x_1 = 2, \quad x_2 = 4

Formula Required: Trinomial Factoring

-2 and -4 multiply to 8 and add to -6.

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

6 Steps

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

x^2 - 6x + 8 = 0

Find two numbers that multiply to $c = 8$ and add up to $b = -6$.

(-2) \times (-4) = 8, \quad (-2) + (-4) = -6

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 - 6(2) + 8 = 4 - 12 + 8 = 0 \;\checkmark \\[6pt] \text{Check } x = 4: \; (4)^2 - 6(4) + 8 = 16 - 24 + 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} = 6, \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 = 2 and x = 4.