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

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

x=−10
, x=8

Answer 1

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

1. **Move the constant to the other side**:
\[
x^2 + 2x = 8
\]

2. **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 \( 1^2 = 1 \).

Add 1 to both sides:
\[
x^2 + 2x + 1 = 8 + 1
\]
Simplifying gives:
\[
(x + 1)^2 = 9
\]

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

4. **Solve for \( x \)**:

a) \( x + 1 = 3 \):
\[
x = 2
\]

b) \( x + 1 = -3 \):
\[
x = -4
\]

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

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