algebra · worked example

Solve x² + 4x + 4 = 0

Method: perfect square trinomial. Verified step-by-step solution with our free AI math solver.
Problem

x2+4x+4=0x^2 + 4x + 4 = 0

Step-by-step solution

  1. Recognise as (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 with a=xa = x, b=2b = 2.

  2. Factor: (x+2)2=0(x + 2)^2 = 0.

  3. Solve: x=−2x = -2 — repeated root.

Answer

x=−2(double root)x = -2 \quad \text{(double root)}

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