Answer
$x= 16$
Work Step by Step
Given \begin{equation}
\sqrt{x-7}-\sqrt{x}=-1.
\end{equation} First rearrange the radical equation and square both sides to eliminate the radical signs. \begin{equation}
\begin{aligned}
\sqrt{x-7}-\sqrt{x}&=-1\\
\sqrt{x-7}&=\sqrt{x}-1\\
\left( \sqrt{x-7} \right)^2&= \left( \sqrt{x}-1\right)^2\\
x-7& = x-2\sqrt{x}+1\\
-8& = -2\sqrt{x}\\
\left(4\right)^2& = \left(\sqrt{x}\right)^2\\
16&= x.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt{16-7}-\sqrt{16}& \stackrel{?}{=} -1 \\
3-4&\stackrel{?}{=} -1 \\
-1& =-1\ \checkmark.
\end{aligned}
\end{equation} The solution is $x= 16$.
