Question

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

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

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

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

x=−2
𝑥
=
−
2
, x=4
𝑥
=
4
x equals negative 2 , x equals 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 \( 1^2 = 1 \).
\[
x^2 + 2x + 1 = 8 + 1
\]
This simplifies to:
\[
(x + 1)^2 = 9
\]

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

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

The solutions to the equation are:
\[
x = 2 \quad \text{and} \quad x = -4
\]

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