a )
\(x+5x^2=0\)
\(\Rightarrow x\left(1+5x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1+5x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\5x=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{5}\end{matrix}\right.\)
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b )
\(x+1=\left(x+1\right)^2\)
\(\Rightarrow\left(x+1\right)-\left(x+1\right)^2=0\)
\(\Rightarrow\left(x+1\right)\left[1-\left(x+1\right)\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\1-\left(x+1\right)=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x+1=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=0\end{matrix}\right.\)
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