Solve the following quadratic equation using square roots: (x+6)exponent2/2 =8 .(1 point)

Question

Responses

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

{−2,−10}
left brace negative 2 comma negative 10 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 quadratic equation \(\frac{(x+6)^2}{2} = 8\) using square roots, we can follow these steps:

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

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

3. Solve for \(x\) for both cases.

   • First case: \[ x + 6 = 4 \] \[ x = 4 - 6 = -2 \]

   • Second case: \[ x + 6 = -4 \] \[ x = -4 - 6 = -10 \]

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

The correct response from your options is: \({−2,−10}\)