Solve the following quadratic equation using square roots: x+6 to the second power/2=8

Question

.(1 point)
Responses

​ {−0.34,−11.66}
​ left brace negative 0.34 comma negative 11.66 right brace

{10,−22}
left brace 10 comma negative 22 right brace

{−2,−10}
left brace negative 2 comma negative 10 right brace

{−1.17,−6.83}

Answer 1

To solve the quadratic equation \(\frac{(x + 6)^2}{2} = 8\), follow these steps:

1. Isolate the squared term: Multiply both sides by 2: \[ (x + 6)^2 = 16 \]

2. Take the square root of both sides: \[ x + 6 = \pm 4 \]

3. Solve for \(x\):

   • For the positive case: \[ x + 6 = 4 \implies x = 4 - 6 = -2 \]

   • For the negative case: \[ x + 6 = -4 \implies x = -4 - 6 = -10 \]

4. Consolidate the answers: The solutions to the equation are \(x = -2\) and \(x = -10\).

Therefore, the solution set is \({-2, -10}\).

The correct response is: \({-2, -10}\)