Question

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

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

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

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

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 right 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 that value to both sides of the equation:

Half of 2 is 1, and \( 1^2 = 1 \). Add 1 to both sides:

\[
x^2 + 2x + 1 = 8 + 1
\]

This simplifies to:

\[
(x + 1)^2 = 9
\]

3. Take the square root of both sides:

\[
x + 1 = \pm 3
\]

4. Solve for \( x \):

- For the positive case:

\[
x + 1 = 3 \implies x = 3 - 1 = 2
\]

- For the negative case:

\[
x + 1 = -3 \implies x = -3 - 1 = -4
\]

So, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are \( x = 2 \) and \( x = -4 \).

Thus, the correct response is:

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