\(x^{50}=x\Leftrightarrow x^{50}-x=90\Leftrightarrow x\left(x^{49}-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^{49}-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x^{49}=1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)