Question

Complete the square to solve the following quadratic equation: x2+2x−8=0.(1 point)
Responses

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

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

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

x=−2, x=4

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. 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 1 to both sides:
\[
x^2 + 2x + 1 = 8 + 1
\]
\[
x^2 + 2x + 1 = 9
\]

5. Now, the left side can be factored as a perfect square:
\[
(x + 1)^2 = 9
\]

6. Take the square root of both sides:
\[
x + 1 = 3 \quad \text{or} \quad x + 1 = -3
\]

7. Solve for \(x\):
\[
x + 1 = 3 \implies x = 2
\]
\[
x + 1 = -3 \implies x = -4
\]

So the solutions to the equation \(x^2 + 2x - 8 = 0\) are:
\[
x = 2 \quad \text{and} \quad x = -4
\]

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