To solve the equation \( 2\left(x-7\right)^{2}=32 \), we can start by isolating the squared term.
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Divide both sides by 2: \[ \left(x-7\right)^{2} = \frac{32}{2} = 16 \]
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Take the square root of both sides: \[ x-7 = \pm \sqrt{16} \]
Since \( \sqrt{16} = 4 \), we have: \[ x-7 = 4 \quad \text{or} \quad x-7 = -4 \]
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Solve for \( x \):
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For \( x-7 = 4 \): \[ x = 4 + 7 = 11 \]
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For \( x-7 = -4 \): \[ x = -4 + 7 = 3 \]
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Therefore, the solutions to the equation \( 2\left(x-7\right)^{2}=32 \) are: \[ \boxed{11} \quad \text{and} \quad \boxed{3} \]