a: \(\Leftrightarrow\left|x+1\right|=-2x-2\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< =-1\\\left(-2x-2\right)^2-\left(x+1\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< =-1\\3\left(x+1\right)^2=0\end{matrix}\right.\Leftrightarrow x=-1\)
b: \(\Leftrightarrow\left(x-3\right)^2=1\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=1\\x-3=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)