Answer
$x=-0.57$
Work Step by Step
To solve the given equation graphically, you have to treat each side of the equation as a function.
Thus, using a graphing utility, graph the functions:
$y=e^x$ (blue graph)
$y=-x$ (the red graph)
(refer to the image below for the graph.
The point/s where the graphs intersect are the points where $x=\ln{(4-x^2)}$.
The x-coordinates of these point are the solutions to the given equation.
Note that the graphs intersect at the point $(-0.567, 0.567)$.
The x-coordinates of these points are $-0.567$.
Rounded-off to two decimal places, the solution to the given equation is:
$x=-0.57$.
