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 negative 10 , x equals 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 to the other side of the equation:
\[
x^2 + 2x = 8
\]

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:
\[
1^2 = 1
\]

4. Add this squared value to both sides:
\[
x^2 + 2x + 1 = 8 + 1
\]
This simplifies to:
\[
(x + 1)^2 = 9
\]

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

6. Solve for \(x\):
- For the positive case:
\[
x + 1 = 3 \implies x = 3 - 1 = 2
\]
- For the negative case:
\[
x + 1 = -3 \implies x = -3 - 1 = -4
\]

Thus, the solutions to the equation \(x^2 + 2x - 8 = 0\) are:
\[
x = 2, x = -4
\]

The correct responses are:
- \(x = 2, x = -4\)
- \(x \text{ equals } 2, x \text{ equals } -4\)

**Both are valid responses to select from the options provided.**