\[\sqrt{x} = a - 1\]
\[x = (a - 1)^{2}.\]
\[a < 1 \Longrightarrow нет\ решения.\]
\[a = 1 \Longrightarrow x = 0\]
\[a > 1 \Longrightarrow x = (a - 1)^{2}.\]