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

Question

.(1 point)
Responses

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

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

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

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 of the equation: \[ x^2 + 2x = 8 \]

2. Take the coefficient of \( x \) (which is 2), divide it by 2 (getting 1), and square it (getting 1). Add this value to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

3. The left side factors as \( (x + 1)^2 \): \[ (x + 1)^2 = 9 \]

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

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

Thus, the solutions are:

\[ x = 2, \quad x = -4 \]

The correct response is:

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