Solve the following quadratic equation using square roots: (x+6)^2/2=8

Question

.(1 point)
Responses

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

{−1.17,−6.83}
left brace negative 1.17 comma negative 6.83 right brace

​ {−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

Answer 1

To solve the equation \(\frac{(x+6)^2}{2}=8\), we start by eliminating the fraction:

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

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

3. Now we can solve for \(x\) by separating into two cases:

Case 1: \[ x + 6 = 4 \] Subtract 6 from both sides: \[ x = 4 - 6 = -2 \]

Case 2: \[ x + 6 = -4 \] Subtract 6 from both sides: \[ x = -4 - 6 = -10 \]

Thus, the solutions to the equation are: \[ { -2, -10 } \]

So, the correct response is: \[ {−2,−10} \]