Answer
$x=4$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{13-x}=x-1
,$ then the solution/s is/are
\begin{array}{l}\require{cancel}
13-x=(x)^2+2(x)(-1)+(-1)^2
\\\\
13-x=x^2-2x+1
\\\\
-x^2+(-x+2x)+(13-1)=0
\\\\
-x^2+x+12=0
\\\\
x^2-x-12=0
\\\\
(x-4)(x+3)=0
\\\\
x=\{ -3, 4 \}
.\end{array}
Upon checking, only $
x=4
$ satisfies the original equation.