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=10 , x=−8 x equals 10 , x equals negative 8 x=−2 , x=4 x equals negative 2 , x equals 4 x=2 , x=−4

Answer 1

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

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

2. To complete the square, take half of the coefficient of \( x \) (which is 2), square it, and add it to both sides. Half of 2 is 1, and squaring it gives \( 1^2 = 1 \):
\[
x^2 + 2x + 1 = 8 + 1
\]
This simplifies to:
\[
(x + 1)^2 = 9
\]

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

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

Thus, the solutions to the equation are:
\[
x = 2, \quad x = -4
\]

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