If \log_{10}[995+\sqrt{x^{2}-12x+60}]=3, then what is the sum of the roots of the equation?

Explanation

\log_{10}[995+\sqrt{x^2-12x+60}] = 3 \implies 995+\sqrt{x^2-12x+60} = 1000 \implies \sqrt{x^2-12x+60} = 5. Squaring gives x^2-12x+60=25 \implies x^2-12x+35=0. Sum of roots is -\frac{-12}{1} = 12.

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