Completing the Square & the Quadratic Formula Quick Check

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

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

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

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

x=2, x=−4
x equals 2 , x equals negative 4
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Answer 1

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

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

2. Complete the square: Take the coefficient of \(x\), which is 2, halve it to get 1, and then square it to get 1. Add this square to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] This simplifies to: \[ (x + 1)^2 = 9 \]

3. Take the square root of both sides: \[ x + 1 = \pm 3 \]

4. Solve for \(x\):

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

Thus, the solutions to the equation are: \[ x = 2, \quad x = -4 \]

Therefore, the correct answer is: x=2, x=−4