What is the solution set of the equation x^2 + 4x + 4 = 0?

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Question: What is the solution set of the equation x^2 + 4x + 4 = 0?

Options:

Correct Answer: {-2, -2}

Solution:

The equation factors to (x + 2)^2 = 0, giving a double root x = -2.

What is the solution set of the equation x^2 + 4x + 4 = 0?

What is the solution set of the equation x^2 + 4x + 4 = 0?

Step 1: Start with the equation x^2 + 4x + 4 = 0.
Step 2: Recognize that this is a quadratic equation.
Step 3: Look for two numbers that multiply to 4 (the constant term) and add to 4 (the coefficient of x).
Step 4: The numbers 2 and 2 work because 2 * 2 = 4 and 2 + 2 = 4.
Step 5: Rewrite the equation using these numbers: (x + 2)(x + 2) = 0.
Step 6: This can be simplified to (x + 2)^2 = 0.
Step 7: To solve for x, set (x + 2) equal to 0: x + 2 = 0.
Step 8: Solve for x by subtracting 2 from both sides: x = -2.
Step 9: Since this is a double root, the solution set is { -2 }.

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