Question

Completing the Square & the Quadratic Formula Quick Check
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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
x equals negative 2 , x equals 4

x=2, x=−4
x equals 2 , x equals negative 4
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Answer 1

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

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

2. **Complete the square**: Take the coefficient of \(x\), which is 2, halve it to get 1, and then square it to get 1. Add this square to both sides:
\[
x^2 + 2x + 1 = 8 + 1
\]
This simplifies to:
\[
(x + 1)^2 = 9
\]

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

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

Thus, the solutions to the equation are:
\[
x = 2, \quad x = -4
\]

Therefore, the correct answer is:
**x=2, x=−4**