To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, follow these steps:
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Take the square root of both sides: \[ x - 18 = \pm \sqrt{196} \]
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Calculate \(\sqrt{196}\): \[ \sqrt{196} = 14 \]
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Set up the two equations from the result: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]
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Solve each equation:
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For \(x - 18 = 14\): \[ x = 18 + 14 = 32 \]
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For \(x - 18 = -14\): \[ x = 18 - 14 = 4 \]
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The solutions are: \[ x = 32 \quad \text{and} \quad x = 4 \]
Thus, the correct answer is \({32, 4}\).
So the answer is: {32, 4}.