To solve the equation \((x + 3)^2 = 36\) using square roots, follow these steps:
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Take the square root of both sides: \[ x + 3 = \pm 6 \] This means we have two cases to consider: \[ x + 3 = 6 \quad \text{and} \quad x + 3 = -6 \]
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Solve each case separately:
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First case: \(x + 3 = 6\) \[ x = 6 - 3 = 3 \]
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Second case: \(x + 3 = -6\) \[ x = -6 - 3 = -9 \]
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Write the solutions: The solutions to the equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]
Thus, the final answer is: \[ x = 3 \quad \text{and} \quad x = -9 \]
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