algebra · worked example

Solve x² + 2x + 1 = 0

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

x2+2x+1=0x^2 + 2x + 1 = 0

Step-by-step solution

  1. Recognise x2+2x+1x^2 + 2x + 1 as a perfect square trinomial matching (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2 with a=xa = x, b=1b = 1.

  2. Factor: (x+1)2=0(x + 1)^2 = 0.

  3. Take the square root of both sides: x+1=0x + 1 = 0.

  4. Solve: x=−1x = -1 — a repeated root (multiplicity 2).

Answer

x=−1(double root)x = -1 \quad \text{(double root)}

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