Algebra • Step-by-Step

Solve x² + 4x + 4 = 0 with Steps

Step-by-step solution for x² + 4x + 4 = 0. Shows discriminant Δ = 0 and perfect square trinomial (x + 2)² = 0 with repeated root x = -2.

Problem Statement

x^2 + 4x + 4 = 0

Final Result

x = -2

Formula Required: Perfect Square Trinomial

When b² - 4ac = 0, the quadratic is a perfect square with a single repeated root.

x^2 + 2kx + k^2 = (x + k)^2 = 0

6 Steps

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

x^2 + 4x + 4 = 0

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

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

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

(x + 2)^2 = 0

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

x + 2 = 0 \implies x = -2

Verify the solution by substituting back into the original equation.

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

It has one unique real root with multiplicity 2: x = -2, since (x + 2)² = 0.