#### Answer

$x=\left\{-2.31, 1.79\right\}$.

#### Work Step by Step

To solve the given equation graphically, perform the following steps:
(1) Graph the functions $y=x^4$ (red graph) and $y=16-x^3$ (blue graph) using a graphing utility. Refer to the image below for the graph.
(2) Identify the point/s where the graphs intersect each other. These are the points where the value of $x^4$ and $16-x^3$ are equal.
The x-coordinates of these points are the solutions to the given equation.
Notice that the graphs intersect each other at $(-2.306, 28.255)$ and $(1.79, 10.265)$.
This means that the solutions to the given equation are: $-2.306$, and $1.79$.
Thus, the solutions, rounded to two decimal places when needed, are:
$x=\left\{-2.31, 1.79\right\}$.