Answer
$5$
Work Step by Step
$x-\sqrt (19-2x) -2 = 0$
$x-2 = \sqrt (19-2x) $
Squaring on both sides.
$(x-2)^{2} = 19-2x$
Using $(a-b)^{2} = a^{2} -2ab +b^{2} $
$(x-2)^{2} = 19-2x$
$x^{2}-4x+4= 19-2x$
$x^{2}-4x+4- 19+2x=0$
$x^{2}-2x-15=0$
By factoring,
$(x-5)(x+3)=0$
$x=5$ or $x=-3$
Substituting $x=5$ and $x=-3$ in the given equation, $x=5$ only satisfies the equation. So, $x=5$ is the solution.