Question:

If x2 + 4x + 4 = 0, what is x?

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Recognize perfect square trinomials to simplify quadratic solutions.
Updated On: Aug 11, 2025
  • -1
  • -2
  • -3
  • -4
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The Correct Option is B

Solution and Explanation

Step-by-step Solution

  1. Recognize a perfect square.
    x2 + 4x + 4 = (x + 2)2 because 4x = 2·2·x and 4 = 22.
  2. Set the square equal to zero.
    (x + 2)2 = 0 ⇒ x + 2 = 0 (a square is zero only when the base is zero).
  3. Solve for x.
    x = -2.
  4. Alternate check (quadratic formula).
    For ax2 + bx + c = 0, with a = 1, b = 4, c = 4:
    Discriminant D = b2 − 4ac = 16 − 16 = 0.
    x = (−b ± √D) / (2a) = (−4 ± 0) / 2 = −2. (Double root)

Final Answer

x = −2Correct option.

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