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What are the solutions to the equation x^2 + 4x + 4 = 0?

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Question: What are the solutions to the equation x^2 + 4x + 4 = 0?

Options:

  1. x = -2
  2. x = 2
  3. x = 0
  4. x = -4

Correct Answer: x = -2

Solution: 

This factors to (x + 2)(x + 2) = 0, so the double root is x = -2.

What are the solutions to the equation x^2 + 4x + 4 = 0?

Practice Questions

Q1
What are the solutions to the equation x^2 + 4x + 4 = 0?
  1. x = -2
  2. x = 2
  3. x = 0
  4. x = -4

Questions & Step-by-Step Solutions

What are the solutions to the equation x^2 + 4x + 4 = 0?
Correct Answer: x = -2
  • Step 1: Start with the equation x^2 + 4x + 4 = 0.
  • Step 2: Look for two numbers that multiply to 4 (the last number) and add to 4 (the middle number).
  • Step 3: The numbers 2 and 2 work because 2 * 2 = 4 and 2 + 2 = 4.
  • Step 4: Rewrite the equation using these numbers: (x + 2)(x + 2) = 0.
  • Step 5: This can also be written as (x + 2)^2 = 0.
  • Step 6: To find the value of x, set x + 2 = 0.
  • Step 7: Solve for x by subtracting 2 from both sides: x = -2.
  • Step 8: Since this is a double root, the solution is x = -2.
  • Factoring Quadratic Equations – The question tests the ability to factor a quadratic equation and identify its roots.
  • Identifying Double Roots – The question assesses understanding of double roots in a quadratic equation, where the same root appears twice.
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