Question

Complete the square to solve the following quadratic equation: x2+2x−8=0.(1 point)
Responses

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

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

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

x=−2, x=4

Answer 1

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

1. **Move the constant term to the right side of the equation**:
\[
x^2 + 2x = 8
\]

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

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

4. **Solve for \(x\)**:
- For \(x + 1 = 3\):
\[
x = 3 - 1 = 2
\]

- For \(x + 1 = -3\):
\[
x = -3 - 1 = -4
\]

So the solutions to the equation \(x^2 + 2x - 8 = 0\) are:
\[
x = 2 \quad \text{and} \quad x = -4
\]

Thus, the correct response is:
**x=2, x=−4**
or
**x equals 2, x equals negative 4**