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=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

Answer 1

To solve the quadratic equation \( x^2 + 2x - 8 = 0 \) by completing the square, 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. 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. Half of 2 is 1, and \(1^2 = 1\).
\[
x^2 + 2x + 1 = 8 + 1
\]
\[
x^2 + 2x + 1 = 9
\]

4. The left side factors as:
\[
(x + 1)^2 = 9
\]

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

6. Solve for \(x\):
- 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 to the equation \( x^2 + 2x - 8 = 0 \) are:
\[
x = 2, \quad x = -4
\]

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