Let's simplify the expression step by step.
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Start with the left side: \[ (-7 - (-2))^2 + (6 - (-6))^2 \]
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Calculate \(-7 - (-2)\): \[ -7 + 2 = -5 \]
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Now square it: \[ (-5)^2 = 25 \]
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Next, calculate \(6 - (-6)\): \[ 6 + 6 = 12 \]
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Now square it: \[ (12)^2 = 144 \]
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Combine the two results: \[ 25 + 144 = 169 \]
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Now we can move to the right side: \[ \sqrt{(-5)^2 + 12^2} \]
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Calculate \((-5)^2\): \[ 25 \]
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Calculate \(12^2\): \[ 144 \]
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Combine these results: \[ 25 + 144 = 169 \]
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Now take the square root: \[ \sqrt{169} = 13 \]
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Therefore, we have: \[ [(-7 - (-2))^2 + (6 - (-6))^2] = \sqrt{(-5)^2 + 12^2} = 13 \]
The final answer is: \[ \boxed{13} \]