To solve the equation \(\frac{(x + 6)^2}{2} = 8\), we can follow these steps:
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Eliminate the fraction by multiplying both sides by 2:
\[ (x + 6)^2 = 16 \]
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Take the square root of both sides, remembering to consider both the positive and negative roots:
\[ x + 6 = 4 \quad \text{or} \quad x + 6 = -4 \]
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Solve for \(x\) in each case:
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For the first case: \[ x + 6 = 4 \implies x = 4 - 6 \implies x = -2 \]
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For the second case: \[ x + 6 = -4 \implies x = -4 - 6 \implies x = -10 \]
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Write the solutions:
The solutions to the equation \(\frac{(x + 6)^2}{2} = 8\) are: \[ x = -2 \quad \text{and} \quad x = -10 \]
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