Answer
$x=5$
Work Step by Step
Isolate the square root on one side. Then square both sides and put all terms on one side. Factor by trial and error to solve for $x$. One of the answers does not work.
$x-\sqrt{x+11}=1$
$x-1=\sqrt {x+11}$
$(x-1)^2=(\sqrt {x+11})^2$
$x^2-2x+1=x+11$
$x^2-3x-10=0$
$(x-5)(x+2)=0$
$x=-2,5$
$-2-\sqrt {-2+11}\ne1$
$x=5$
