To solve the quadratic equation \((x−18)^2 = 196\) using square roots, we can follow these steps:
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Take the square root of both sides:
\[ x - 18 = \pm \sqrt{196} \]
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Calculate the square root of 196:
\(\sqrt{196} = 14\)
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Set up the two equations:
\[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]
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Solve each equation:
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For \(x - 18 = 14\): \[ x = 14 + 18 = 32 \]
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For \(x - 18 = -14\): \[ x = -14 + 18 = 4 \]
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List the solutions: The solutions to the equation are \(x = 32\) and \(x = 4\).
Thus, the solution set is \({32, 4}\).
The correct response is:
\({32, 4}\) left brace 32 comma 4 right brace.