Complete the square to solve the following quadratic equation: x2+2x−8=0

Question

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

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

x=−2
𝑥
=
−
2
, x=4

Answer 1

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

1. Start with the original 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: \[ x^2 + 2x + 1 = 8 + 1 \]

4. This simplifies to: \[ (x + 1)^2 = 9 \]

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

6. Solve for \( x \): \[ x = 3 - 1 \quad \text{or} \quad x = -3 - 1 \] \[ x = 2 \quad \text{or} \quad x = -4 \]

Thus, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are: \[ x = 2 \quad \text{and} \quad x = -4 \]

The correct response from the provided options is: x=2, x=−4 (x equals 2, x equals negative 4).