To solve the quadratic equation \((x - 6)^2 = 51\) using square roots, follow these steps:
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Take the square root of both sides of the equation: \[ x - 6 = \pm \sqrt{51} \]
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Solve for \(x\) by isolating it: \[ x = 6 \pm \sqrt{51} \]
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Calculate \(\sqrt{51}\): \[ \sqrt{51} \approx 7.14 \]
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Now substitute back to find the two possible values of \(x\): \[ x = 6 + 7.14 \quad \text{and} \quad x = 6 - 7.14 \]
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For \(x = 6 + 7.14\): \[ x \approx 13.14 \]
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For \(x = 6 - 7.14\): \[ x \approx -1.14 \]
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Thus, the solutions to the equation \((x - 6)^2 = 51\) are approximately: \[ x \approx 13.14 \quad \text{and} \quad x \approx -1.14 \]