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

Question

Responses

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

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

x=−2, x=4
x equals negative 2 , x equals 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. Start with the equation: \[ x^2 + 2x - 8 = 0 \]

2. Move the constant to the other side of the equation: \[ x^2 + 2x = 8 \]

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 this squared value to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] This simplifies to: \[ (x + 1)^2 = 9 \]

5. Now, take the square root of both sides: \[ x + 1 = \pm 3 \]

6. Solve for \(x\):

   • For the positive case: \[ x + 1 = 3 \implies x = 3 - 1 = 2 \]
   • For the negative case: \[ x + 1 = -3 \implies x = -3 - 1 = -4 \]

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

The correct responses are:

• \(x = 2, x = -4\)
• \(x \text{ equals } 2, x \text{ equals } -4\)

Both are valid responses to select from the options provided.