Answer
$2.2824$
Refer to the graph below.
Work Step by Step
Use a graphing calculator to graph $y=\pi\cdot \sin^{-1}{(0.2x)}-3$ and $y=-\sqrt{x}$.
The x-coordinate of the point of intersection, which is $(2.2824, -1.5108)$. is the solution to the equation.
Therefore, the solution to the given equation is $2.2824$.