To simplify the expression \(-6\sqrt{21} - 2\sqrt{84}\), we first simplify \(\sqrt{84}\).
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Find the prime factorization of 84: \[ 84 = 2^2 \times 3 \times 7 \]
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Now, take the square root of each factor: \[ \sqrt{84} = \sqrt{2^2 \times 3 \times 7} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{7} = 2\sqrt{21} \]
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Substitute \(\sqrt{84}\) back into the expression: \[ -6\sqrt{21} - 2\sqrt{84} = -6\sqrt{21} - 2(2\sqrt{21}) = -6\sqrt{21} - 4\sqrt{21} \]
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Now, combine the like terms: \[ -6\sqrt{21} - 4\sqrt{21} = (-6 - 4)\sqrt{21} = -10\sqrt{21} \]
Thus, the final answer is: \[ \boxed{-10\sqrt{21}} \]