Question

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

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

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

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

2. Take the coefficient of \( x \) (which is 2), divide it by 2, and square it:
\[
\left(\frac{2}{2}\right)^2 = 1
\]

3. Add this square to both sides of the equation:
\[
x^2 + 2x + 1 = 8 + 1
\]
\[
x^2 + 2x + 1 = 9
\]

4. Now, factor the left side:
\[
(x + 1)^2 = 9
\]

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

6. Solve for \( x \):
\[
x = 3 - 1 \quad \Rightarrow \quad x = 2
\]
\[
x = -3 - 1 \quad \Rightarrow \quad x = -4
\]

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

So the correct response is:
**x=2, x=−4** (x equals 2 , x equals negative 4).