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

Question

Responses

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

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

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

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

Answer 1

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

1. Move the constant to the other side: \( x^2 + 2x = 8 \)

2. 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 \( 1^2 = 1 \).

   Add 1 to both sides: \[ x^2 + 2x + 1 = 8 + 1 \]

3. Rewrite the left side as a square: \[ (x + 1)^2 = 9 \]

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

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

   From \( x + 1 = -3 \): \[ x = -3 - 1 = -4 \]

The solutions to the equation are \( x = 2 \) and \( x = -4 \).

So the correct answer is: x = 2, x = −4.