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

Question

Responses

{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}
left brace negative 1.17 comma negative 6.83 right brace

​ {−0.34,−11.66}

Answer 1

To solve the quadratic equation, we need to isolate the variable x.

First, let's simplify the equation:
(x+6)^2/2 = 8

Next, let's multiply both sides of the equation by 2 to get rid of the fraction:
2 * (x+6)^2/2 = 8 * 2
(x+6)^2 = 16

Now, let's take the square root of both sides of the equation:
√(x+6)^2 = √16
x+6 = ±√16

Simplifying further:
x+6 = ±4

Now, let's solve for x:
x = -6 + 4 or x = -6 - 4
x = -2 or x = -10

Therefore, the solution to the quadratic equation is {−2,−10}.