If \(x^2 + 2x + 1 = 0\), what is \(x\)?

If \(x^2 + 2x + 1 = 0\), what is \(x\)?

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(-1\)

Answer: (D)

To solve the equation \(x^2 + 2x + 1 = 0\), we can recognize that this is a perfect square trinomial. The expression can be factored as \((x + 1)^2 = 0\). This means that the solution to the equation occurs when the squared term is equal to zero. Therefore, we set the factor equal to zero: \[ x + 1 = 0 \] Solving for \(x\) gives: \[ x = -1 \] Thus, the value of \(x\) that satisfies the equation \(x^2 + 2x + 1 = 0\) is \(-1\). This indicates that the answer is indeed correct. The interpretation of the equation makes it clear that there is a single solution, not multiple solutions, hence confirming that \(-1\) is the only value for \(x\) that ensures that the original equation holds true.

To solve the equation (x^2 + 2x + 1 = 0), we can recognize that this is a perfect square trinomial. The expression can be factored as ((x + 1)^2 = 0).

This means that the solution to the equation occurs when the squared term is equal to zero. Therefore, we set the factor equal to zero:

[

x + 1 = 0

]

Solving for (x) gives:

[

x = -1

]

Thus, the value of (x) that satisfies the equation (x^2 + 2x + 1 = 0) is (-1). This indicates that the answer is indeed correct. The interpretation of the equation makes it clear that there is a single solution, not multiple solutions, hence confirming that (-1) is the only value for (x) that ensures that the original equation holds true.