Question

Complete the square to solve the following quadratic equation: x^2+2x−8=0.(1 point)
Responses

x=2, x=−4
x equals 2 , x equals negative 4

x=−2, x=4
x equals negative 2 , x equals 4

x=−10, x=8
x equals negative 10 , x equals 8

x=10, x=−8

Answer 1

To complete the square for the given quadratic equation \( x^2 + 2x - 8 = 0 \), follow these steps:

1. **Rearrange the equation**:
\[
x^2 + 2x = 8
\]

2. **Complete the square**:
- Take the coefficient of \( x \) (which is \( 2 \)), divide by \( 2 \) to get \( 1 \), and then square it to get \( 1^2 = 1 \).
- Add \( 1 \) to both sides of the equation:
\[
x^2 + 2x + 1 = 8 + 1
\]
Simplifying gives:
\[
(x + 1)^2 = 9
\]

3. **Take the square root of both sides**:
\[
x + 1 = \pm 3
\]

4. **Solve for \( x \)**:
- First solution:
\[
x + 1 = 3 \implies x = 3 - 1 = 2
\]
- Second solution:
\[
x + 1 = -3 \implies x = -3 - 1 = -4
\]

So the solutions are \( x = 2 \) and \( x = -4 \).

Thus, the correct response is:
**x equals 2, x equals negative 4**.