To solve the quadratic equation \((x + 3)^2 = 36\) using square roots, follow these steps:
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Take the square root of both sides: \[ x + 3 = \pm \sqrt{36} \]
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Calculate the square root: \[ x + 3 = \pm 6 \]
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Separate into two equations:
- First equation:
\[ x + 3 = 6 \] - Second equation:
\[ x + 3 = -6 \]
- First equation:
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Solve each equation:
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From \(x + 3 = 6\): \[ x = 6 - 3 \] \[ x = 3 \]
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From \(x + 3 = -6\): \[ x = -6 - 3 \] \[ x = -9 \]
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Final Solutions: So, the solutions to the quadratic equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]