1) \(5x^2-2x-7=0\)
\(\Leftrightarrow5x^2+5x-7x-7=0\)
\(\Leftrightarrow5x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(5x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\5x-7=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{7}{5}\end{matrix}\right.\)
2) \(x^2-10x-11=0\)
\(\Leftrightarrow x^2+x-11x-11=0\)
\(\Leftrightarrow x\left(x+1\right)-11\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-11\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-11=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=11\end{matrix}\right.\)
3) \(x^2-7x-8=0\)
\(\Leftrightarrow x^2+x-8x-8=0\)
\(\Leftrightarrow x\left(x+1\right)-8\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-8=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=8\end{matrix}\right.\)
4) \(x^2+9x+8=0\)
\(\Leftrightarrow x^2+x+8x+8=0\)
\(\Leftrightarrow x\left(x+1\right)+8\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+8=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-8\end{matrix}\right.\)
5) \(x^2-5x-6=0\)
\(\Leftrightarrow x^2+x-6x-6=0\)
\(\Leftrightarrow x\left(x+1\right)-6\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=6\end{matrix}\right.\)
