Giải:

a) \(x^2+5x=6\)

\(\Leftrightarrow x^2+5x-6=0\)

\(\Leftrightarrow x^2+6x-x-6=0\)

\(\Leftrightarrow\left(x^2+6x\right)-\left(x+6\right)=0\)

\(\Leftrightarrow x\left(x+6\right)-\left(x+6\right)=0\)

\(\Leftrightarrow\left(x+6\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+6=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=1\end{matrix}\right.\)

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b) \(x^2-2015x+2014=0\)

\(\Leftrightarrow x^2-2014x-x+2014=0\)

\(\Leftrightarrow\left(x^2-2014x\right)-\left(x-2014\right)=0\)

\(\Leftrightarrow x\left(x-2014\right)-\left(x-2014\right)=0\)

\(\Leftrightarrow\left(x-2014\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2014=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2014\\x=1\end{matrix}\right.\)

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