To solve the equation \((x - 5)^2 = 3\), we can start by taking the square root of both sides. Remember that taking the square root introduces both a positive and a negative solution.
\[ x - 5 = \pm \sqrt{3} \]
Next, we solve for \(x\) in both cases:
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When \(x - 5 = \sqrt{3}\): \[ x = 5 + \sqrt{3} \]
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When \(x - 5 = -\sqrt{3}\): \[ x = 5 - \sqrt{3} \]
Thus, the solutions to the equation \((x - 5)^2 = 3\) are:
\[ x = 5 + \sqrt{3} \quad \text{and} \quad x = 5 - \sqrt{3} \]