a) `x^2 +x =0`
`=> x. (x+1)=0`
`=>`$\left[\begin{matrix} x=0\\ x+1=0\end{matrix}\right.$
`=>` $\left[\begin{matrix} x=0\\ x=-1\end{matrix}\right.$
b) `(2x+1)^2 =25`
`(2x+1)^2=(±5)^2`
`=>`$\left[\begin{matrix} 2x+1=5\\ 2x+1=-5\end{matrix}\right.$
`=>`$\left[\begin{matrix} 2x=4\\ 2x=-6\end{matrix}\right.$
`=>`$\left[\begin{matrix} x=2\\ x=-3\end{matrix}\right.$
c) `(2x-3)^2=36`
`(2x-3)^2=(±6)^2`
`=>` $\left[\begin{matrix} 2x-3=6\\ 2x-3=-6\end{matrix}\right.$
`=>` $\left[\begin{matrix} 2x=9\\ 2x=-3\end{matrix}\right.$
`=>` $\left[\begin{matrix} x=9/2\\ x=-3/2\end{matrix}\right.$
d) `(2x-1)^3=-8`
`(2x-1)^3=-2^3`
`=> 2x-1 =-2`
`=> 2x =-1`
`=> x =-1/2`
e) `(x-1)^(x-2)=(x-1)^(x-4)`
`(x-1)^(x-2) - (x-1)^{(x-4)}=0`
`(x-1)^(x-4).[(x-1)^2 -1]=0`
`=>` $\left[\begin{matrix} (x-1)^{(x-4)} =0\\ (x-1)^2 -1=0\end{matrix}\right.$
`=>` $\left[\begin{matrix} x-1=0\\ (x-1)^2=1\end{matrix}\right.$
`=>` $\left[\begin{matrix} x=1\\ (x-1)^2=(±1)^2\end{matrix}\right.$
`=>` $\left[\begin{matrix} x=1\\ x-1=1 ;x-1 =-1\end{matrix}\right.$
`=>` $\left[\begin{matrix} x=1\\ x=2;x=0\end{matrix}\right.$
