What is the solution to the equation 4x^2 + 8x + 4 = 0?

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Question: What is the solution to the equation 4x^2 + 8x + 4 = 0?

Options:

Correct Answer: x = -2

Solution:

This can be factored as 4(x^2 + 2x + 1) = 0, which simplifies to 4(x + 1)(x + 1) = 0. Thus, x = -1.

What is the solution to the equation 4x^2 + 8x + 4 = 0?

What is the solution to the equation 4x^2 + 8x + 4 = 0?

Step 1: Start with the equation 4x^2 + 8x + 4 = 0.
Step 2: Notice that all terms can be divided by 4. So, divide the entire equation by 4 to simplify it: x^2 + 2x + 1 = 0.
Step 3: Now, look for two numbers that multiply to 1 (the constant term) and add up to 2 (the coefficient of x). The numbers are 1 and 1.
Step 4: Rewrite the equation using these numbers: (x + 1)(x + 1) = 0.
Step 5: This can also be written as (x + 1)^2 = 0.
Step 6: To find the value of x, set (x + 1) = 0.
Step 7: Solve for x by subtracting 1 from both sides: x = -1.

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