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

Question

Responses

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

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

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

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 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: \[ 1^2 = 1 \]

4. Add 1 to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

5. Now, the left side can be factored as a perfect square: \[ (x + 1)^2 = 9 \]

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

7. Solve for \(x\): \[ x + 1 = 3 \implies x = 2 \] \[ x + 1 = -3 \implies x = -4 \]

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

The correct response is: x equals 2, x equals negative 4.