\[(a - 2)\sqrt{x} = a - 2\]
\[\sqrt{x} = \frac{a - 2}{a - 2}\text{\ \ }\]
\[\sqrt{x} = 1\]
\[\ x = 1.\]
\[a = 2 \Longrightarrow x - любое.\]
\[a \neq 2 \Longrightarrow x = 1.\]