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

{−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

{−2,−10}

1 answer

To solve the equation \((x + 6)^2 / 2 = 8\), we can start by isolating the squared term.

  1. Multiply both sides by 2 to eliminate the fraction:

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

  1. Now, take the square root of both sides:

\[ x + 6 = \pm 4 \]

  1. This gives us two equations to solve:

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

Second equation: \[ x + 6 = -4 \] Subtracting 6 from both sides: \[ x = -4 - 6 \] \[ x = -10 \]

Thus, the solutions to the equation are:

\[ { -2, -10 } \]

The correct choice from the options given is \({ -2, -10 }\).