Question

Complete the square to identify the two values that solve the quadratic equation x^2 + 8x = 9.
x = ?

Answer 1

Theres only one answer

Answer 2

To solve the quadratic equation \( x^2 + 8x = 9 \) by completing the square, follow these steps:

1. Move the constant term to the other side of the equation:

\[
x^2 + 8x - 9 = 0
\]

2. Isolate the \( x \) terms:

\[
x^2 + 8x = 9
\]

3. Complete the square. Take half of the coefficient of \( x \) (which is 8), square it, and add it to both sides of the equation. Half of 8 is 4, and \( 4^2 = 16 \):

\[
x^2 + 8x + 16 = 9 + 16
\]

4. Simplifying gives:

\[
x^2 + 8x + 16 = 25
\]

5. The left side can be factored as a perfect square:

\[
(x + 4)^2 = 25
\]

6. Now take the square root of both sides:

\[
x + 4 = \pm 5
\]

7. This gives us two equations to solve for \( x \):

- \( x + 4 = 5 \)
- \( x + 4 = -5 \)

8. Solving these:

- For \( x + 4 = 5 \):
\[
x = 5 - 4 = 1
\]

- For \( x + 4 = -5 \):
\[
x = -5 - 4 = -9
\]

Thus, the two values that solve the quadratic equation \( x^2 + 8x = 9 \) are:

\[
x = 1 \quad \text{and} \quad x = -9
\]

Answer 3

I apologize for any confusion. However, the equation \(x^2 + 8x = 9\) actually has two solutions, which are derived through completing the square or using the quadratic formula.

Let me clarify:

1. **Start with the original equation**:
\[
x^2 + 8x - 9 = 0
\]

2. **Using completing the square**, we transformed it into:
\[
(x + 4)^2 = 25
\]

3. **Taking square roots**, we found:
\[
x + 4 = 5 \quad \text{or} \quad x + 4 = -5
\]

which leads to the solutions:
- \( x = 1 \)
- \( x = -9 \)

Thus, the two solutions are **\(x = 1\)** and **\(x = -9\)**.

If you meant that you are looking for just one of the answers, you can choose either \(1\) or \(-9\). Please clarify your question, and I'll be happy to assist!