Completing the Square & the Quadratic Formula Quick Check

Question

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

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

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

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

x=−2
x
=
−
2
, x=4

Answer 1

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

1. Move the constant term 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 then add it to both sides. Half of 2 is 1, and \( 1^2 = 1 \).
   \[ x^2 + 2x + 1 = 8 + 1 \] This simplifies to:
   \[ (x + 1)^2 = 9 \]

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

4. Solve for \( x \):

   • If \( x + 1 = 3 \), then \( x = 3 - 1 = 2 \).
   • If \( x + 1 = -3 \), then \( x = -3 - 1 = -4 \).

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

Thus, the correct response is: x = 2, x = -4.