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

1. Start with the equation:
\[
x^2 + 2x - 8 = 0
\]

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

3. 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 \(1\):
\[
x^2 + 2x + 1 = 8 + 1
\]

4. Rewrite the left side as a square:
\[
(x + 1)^2 = 9
\]

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

6. Solve for \(x\) by isolating it:
\[
x + 1 = 3 \implies x = 3 - 1 = 2
\]
\[
x + 1 = -3 \implies x = -3 - 1 = -4
\]

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

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