To solve the quadratic equation \((x+3)^2 = 36\) using square roots, we can follow these steps:
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Take the square root of both sides: \[ \sqrt{(x+3)^2} = \sqrt{36} \] This gives us: \[ x + 3 = 6 \quad \text{or} \quad x + 3 = -6 \]
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Solve for \(x\) in both cases:
For the first case: \[ x + 3 = 6 \] Subtract 3 from both sides: \[ x = 6 - 3 = 3 \]
For the second case: \[ x + 3 = -6 \] 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 \(x = -9\).