Question

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

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

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

x=10, x=−8
x equals 10 , x equals negative 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 to the other side**:
\[
x^2 + 2x = 8
\]

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 and subtract \( 1 \) on the left side:
\[
x^2 + 2x + 1 - 1 = 8
\]
This simplifies to:
\[
(x + 1)^2 - 1 = 8
\]

So, we have:
\[
(x + 1)^2 = 9
\]

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:
\[
x = 2, \quad x = -4
\]

Therefore, the correct response is:
**x=2, x=−4**.