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Solve the quadratic equation x^2 + 6x + 9 = 0.

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Question: Solve the quadratic equation x^2 + 6x + 9 = 0.

Options:

  1. x = -3
  2. x = 3
  3. x = -6
  4. x = 6

Correct Answer: x = -3

Solution:

This can be factored as (x + 3)(x + 3) = 0. Therefore, x + 3 = 0 gives x = -3.

Solve the quadratic equation x^2 + 6x + 9 = 0.

Practice Questions

Q1
Solve the quadratic equation x^2 + 6x + 9 = 0.
  1. x = -3
  2. x = 3
  3. x = -6
  4. x = 6

Questions & Step-by-Step Solutions

Solve the quadratic equation x^2 + 6x + 9 = 0.
  • Step 1: Identify the quadratic equation, which is x^2 + 6x + 9 = 0.
  • Step 2: Look for two numbers that multiply to 9 (the constant term) and add to 6 (the coefficient of x).
  • Step 3: The numbers 3 and 3 work because 3 * 3 = 9 and 3 + 3 = 6.
  • Step 4: Rewrite the equation using these numbers: (x + 3)(x + 3) = 0.
  • Step 5: Set each factor equal to zero: x + 3 = 0.
  • Step 6: Solve for x by subtracting 3 from both sides: x = -3.
  • Factoring Quadratic Equations – The process of rewriting a quadratic equation in the form of a product of two binomials.
  • Finding Roots – Determining the values of x that satisfy the equation by setting each factor to zero.
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