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: \[ \sqrt{(x + 3)^2} = \sqrt{36} \]
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This gives: \[ x + 3 = \pm 6 \]
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Now, split it into two separate equations:
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For the positive case: \[ x + 3 = 6 \] Subtracting 3 from both sides, we get: \[ x = 6 - 3 = 3 \]
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For the negative case: \[ x + 3 = -6 \] Subtracting 3 from both sides, we get: \[ x = -6 - 3 = -9 \]
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Thus, the solutions to the equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]
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