\(-12x^2+71x+100=0\)
\(\Leftrightarrow-12\left(x^2-\frac{71}{12}x-\frac{25}{3}\right)=0\)
\(\Leftrightarrow x^2-\frac{71}{12}x-\frac{25}{3}=0\)
\(\Leftrightarrow x^2-2\cdot x\cdot\frac{71}{24}+\frac{5041}{576}-\frac{9841}{576}=0\)
\(\Leftrightarrow\left(x-\frac{71}{24}\right)^2=\frac{9841}{576}\)
\(\Leftrightarrow x-\frac{71}{24}=\frac{\pm\sqrt{9841}}{24}\)
\(\Leftrightarrow x=\frac{71\pm\sqrt{9841}}{24}\)
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