\(4x^3+5x^2-x=0\)
\(\Leftrightarrow x\left(4x^2+5x-1\right)=0\)
\(\Leftrightarrow x\left[\left(2x\right)^2+2\cdot2x\cdot\dfrac{5}{4}+\dfrac{25}{16}-\dfrac{41}{16}\right]=0\)
\(\Leftrightarrow x\left[\left(2x+\dfrac{5}{4}\right)^2-\dfrac{41}{16}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(2x-\dfrac{5}{4}\right)^2=\left(\dfrac{\pm\sqrt{41}}{4}\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{\pm\sqrt{41}+5}{8}\end{matrix}\right.\)
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