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 of the equation. Remember to consider both the positive and negative roots: \[ x + 3 = \pm 6 \]
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This gives us two separate equations to solve:
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For the positive root: \[ x + 3 = 6 \] Subtract 3 from both sides: \[ x = 6 - 3 = 3 \]
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For the negative root: \[ x + 3 = -6 \] Subtract 3 from both sides: \[ x = -6 - 3 = -9 \]
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Therefore, the solutions to the equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]
In conclusion, the solutions are \(x = 3\) and \(x = -9\).
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