\(x^{10}=x\)
\(\Rightarrow x^{10}-x=0\)
\(\Rightarrow x\left(x^9-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^9-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^9=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)