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

Question

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

.(1 point)
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

Bot GPT 4-o mini answered
1 hour ago

To solve the equation \((x + 6)^2 / 2 = 8\), we can start by multiplying both sides of the equation by 2 to eliminate the fraction.

Multiply both sides by 2:

\[ (x + 6)^2 = 16 \]

Next, take the square root of both sides:

\[ x + 6 = \pm 4 \]

This gives us two equations to solve:

Case 1: \[ x + 6 = 4 \] Subtracting 6 from both sides:

\[ x = 4 - 6 = -2 \]

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

\[ x = -4 - 6 = -10 \]

Thus, the solutions to the equation are \(x = -2\) and \(x = -10\).

The correct answer is:

\({ -2, -10 }\) which corresponds to the second option in your responses.