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

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:
\[
x^2 + 8x - 9 = 0
\]
or, equivalently,
\[
x^2 + 8x = 9.
\]

2. To complete the square, take the coefficient of \(x\) (which is 8), divide it by 2, and square it:
\[
\left(\frac{8}{2}\right)^2 = 4^2 = 16.
\]

3. Add and subtract this square (16) on the left side of the equation:
\[
x^2 + 8x + 16 - 16 = 9,
\]
or rewriting this gives:
\[
(x + 4)^2 - 16 = 9.
\]

4. Now, rearrange the equation:
\[
(x + 4)^2 = 9 + 16,
\]
which simplifies to:
\[
(x + 4)^2 = 25.
\]

5. Take the square root of both sides:
\[
x + 4 = \pm 5.
\]

6. Now, solve for \(x\) by isolating it in both cases:
\[
x + 4 = 5 \quad \Rightarrow \quad x = 5 - 4 = 1,
\]
and
\[
x + 4 = -5 \quad \Rightarrow \quad x = -5 - 4 = -9.
\]

Thus, the two values that solve the quadratic equation \(x^2 + 8x = 9\) are:
\[
x = 1 \quad \text{and} \quad x = -9.
\]

Make sure to combine all constants using the inverse of addition or subtraction before determining the square root.

Let's go through the process of completing the square while paying closer attention to combining the constants properly before determining the square root.

Starting with the equation:

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

1. **Move the constant to the other side:**

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

or, in the original form:

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

2. **Complete the square:**
- Take the coefficient of \(x\), which is \(8\), divide by \(2\) to get \(4\), and then square it:

\[
\left(\frac{8}{2}\right)^2 = 4^2 = 16
\]

3. **Add and subtract \(16\) on the left side:**

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

This can be rearranged to:

\[
(x + 4)^2 - 16 = 9
\]

4. **Combine constants on the right side:**

Rearrange the equation to isolate the perfect square:

\[
(x + 4)^2 = 9 + 16
\]

Simplifying the right side gives:

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

5. **Take the square root of both sides:**

\[
x + 4 = \pm 5
\]

6. **Solve for \(x\):**

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

\[
x = 5 - 4 = 1
\]

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

\[
x = -5 - 4 = -9
\]

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

\[
\boxed{1} \quad \text{and} \quad \boxed{-9}
\]

Thank you for your guidance, and I hope this process meets your expectations!

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

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

1. **Rearrange the equation:**
Start by moving the constant term to the left side:
\[
x^2 + 8x - 9 = 0
\]
or keeping it in the equation form:
\[
x^2 + 8x = 9.
\]

2. **Complete the square:**
- Take the coefficient of \(x\) (which is \(8\)), divide it by \(2\), and then square it:
\[
\left(\frac{8}{2}\right)^2 = 4^2 = 16.
\]

3. **Add and subtract this square inside the equation:**
We rewrite the equation as:
\[
x^2 + 8x + 16 - 16 = 9,
\]
which simplifies to:
\[
(x + 4)^2 - 16 = 9.
\]

4. **Isolate the squared term:**
Now, move \(-16\) to the right side:
\[
(x + 4)^2 = 9 + 16,
\]
which simplifies to:
\[
(x + 4)^2 = 25.
\]

5. **Take the square root of both sides:**
\[
x + 4 = \pm 5.
\]

6. **Solve for \(x\):**
- For the positive case:
\[
x + 4 = 5 \quad \Rightarrow \quad x = 5 - 4 = 1.
\]
- For the negative case:
\[
x + 4 = -5 \quad \Rightarrow \quad x = -5 - 4 = -9.
\]

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

\[
\boxed{1} \quad \text{and} \quad \boxed{-9}.
\]

its not 1 or -9

Apologies for any confusion in my previous responses. Let's go through the completion of the square step by step once again to ensure accuracy.

We start with the equation:

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

### Step 1: Move the constant to the other side

Let's rearrange it:

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

### Step 2: Complete the square

We need to complete the square for \(x^2 + 8x\).

1. Take the coefficient of \(x\) (which is \(8\)), divide it by \(2\) (giving \(4\)), and square it (giving \(16\)).
2. Rewrite the equation as:

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

Reorganize it to group the completed square:

\[
(x + 4)^2 - 16 = 9
\]

### Step 3: Simplify the equation

Now, add \(16\) to both sides:

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

### Step 4: Take the square root of both sides

Now we take the square root of both sides:

\[
x + 4 = \pm 5
\]

### Step 5: Solve for \(x\)

1. **If \(x + 4 = 5\)**:
\[
x = 5 - 4 = 1
\]

2. **If \(x + 4 = -5\)**:
\[
x = -5 - 4 = -9
\]

Thus, the solutions obtained are indeed:

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

#### Conclusion

If you have indicated that these are incorrect, please let me know the correct values you have or check the values in relation to the given equation \(x^2 + 8x = 9\) to ensure they match the calculation. Thank you for your patience!