Question

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

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

Answer 1

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

1. Rearrange the equation:
\[
x^2 + 2x = 8
\]

2. Complete the square on the left side. Take half of the coefficient of \(x\) (which is \(2\)), square it, and add it to both sides:
\[
\left(\frac{2}{2}\right)^2 = 1
\]
So we 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 \(x\) by isolating \(x\):
- For the positive case:
\[
x + 1 = 3 \quad \Rightarrow \quad x = 3 - 1 = 2
\]
- For the negative case:
\[
x + 1 = -3 \quad \Rightarrow \quad x = -3 - 1 = -4
\]

Thus, the solutions are \(x = 2\) and \(x = -4\).

The correct response is:
**x = 2, x = -4**.