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Completing the Square & the Quadratic Formula Practice
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Complete the square to identify the two values that solve the following quadratic equation: x2+8x=9
.(1 point)
x=
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page 19 of 20

Answer 1

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

1. **Move 9 to the left side of the equation:**

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

2. **Isolate the quadratic and linear terms:**

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

3. **Complete the square:**

To complete the square for the expression \( x^2 + 8x \), 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 squaring it gives 16.

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

Simplifying both sides:

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

4. **Factor the left side:**

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

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

\[
x + 4 = \pm 5
\]

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

From \( x + 4 = 5 \):

\[
x = 5 - 4 = 1
\]

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

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

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

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

If you are looking to fill in the answer:

```
x = 1 or x = -9
```