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

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

x=10, x=−8
x equals 10 , x equals negative 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 right side of the equation:

   \[ x^2 + 2x = 8 \]

2. Identify the coefficient of \( x \) (which is 2), take half of it (which is 1), and square it (which is 1). We will add and subtract this square on the left side of the equation:

   \[ x^2 + 2x + 1 - 1 = 8 \]

   This simplifies to:

   \[ (x + 1)^2 - 1 = 8 \]

3. Rearranging gives:

   \[ (x + 1)^2 = 9 \]

4. Taking the square root of both sides gives:

   \[ x + 1 = 3 \quad \text{or} \quad x + 1 = -3 \]

5. Solving for \( x \) in both scenarios:

   \( x + 1 = 3 \) leads to:

   \[ x = 2 \]

   \( x + 1 = -3 \) leads to:

   \[ x = -4 \]

Thus, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are:

\[ x = 2 \quad \text{and} \quad x = -4 \]

So the correct response is:

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