Question

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

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

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

x=−2, x=4

Answer 1

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

1. Move the constant term to the right side of the equation:
\[
x^2 + 2x = 8
\]

2. To complete the square, take half of the coefficient of \( x \) (which is 2), square it, and then add it to both sides. Half of 2 is 1, and squaring it gives \( 1^2 = 1 \):
\[
x^2 + 2x + 1 = 8 + 1
\]

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

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

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

So, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are \( x = 2 \) and \( x = -4 \).

None of the provided responses are correct. The correct solutions are:

**x = 2, x = -4**.