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: \[ x - 6 = \pm \sqrt{51} \]
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Isolate \(x\): \[ x = 6 \pm \sqrt{51} \]
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Calculate \(\sqrt{51}\): The approximate value of \(\sqrt{51}\) is about 7.14 (calculated using a calculator).
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Now, solve for \(x\): \[ x = 6 + \sqrt{51} \quad \text{and} \quad x = 6 - \sqrt{51} \]
Hence, the two solutions are: \[ x \approx 6 + 7.14 = 13.14 \] \[ x \approx 6 - 7.14 = -1.14 \]
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Final answers: The solutions to the equation are: \[ x \approx 13.14 \quad \text{and} \quad x \approx -1.14 \]
So, rounded to the nearest hundredth, the solutions are \(x \approx 13.14\) and \(x \approx -1.14\).
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