#### Answer

$x=5-\sqrt {41},5+\sqrt {41}$

#### Work Step by Step

When taking the square root of a number, you get a positive and a negative answer.
$-9(x-5)^2=-369$
$(x-5)^2=41$
$x-5=\sqrt {41}$
$x=5+\sqrt {41}$
or
$x-5=-\sqrt {41}$
$x=5-\sqrt {41}$.
So
$x=5-\sqrt {41},5+\sqrt {41}$.