\(4x^2+x-5=0\)
\(\Leftrightarrow\left(4x^2-4x\right)+\left(5x-5\right)=0\)
\(\Leftrightarrow4x\left(x-1\right)+5\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(4x+5\right)=0\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x-1=0\\4x+5=0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=1\\4x=-5\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=1\\x=-\frac{5}{4}\end{matrix}\right.\)
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