\(1+6x-6x^2-x^3=0\)
\(\Leftrightarrow x^2+7x+1-x^3-7x^2-x=0\)
\(\Leftrightarrow\left(x^2+7x+1\right)-x\left(x^2+7x+1\right)=0\)
\(\Leftrightarrow\left(x^2+7x+1\right)\left(1-x\right)=0\)
\(\Leftrightarrow\left[\left(x^2+7x+\frac{49}{4}\right)-\frac{45}{4}\right]\left(1-x\right)=0\)
\(\Leftrightarrow\left[\left(x+\frac{7}{2}\right)^2-\frac{45}{4}\right]\left(1-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{45}-7}{2}\\x=-\frac{\sqrt{45}+7}{2}\\x=1\end{matrix}\right.\)
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