Answer
approximately $\color{blue}{-1.769}$.
Work Step by Step
Using a graphing utility to graph the function
$y=x^3-2x+2$
(refer to the attached image below for the graph)
The solution to the given equation is the x-coordinate of the point where the graph is equal to zero.
Note that the graph's value is zero at the point $(-1.769, 0)$.
Therefore, the solution to the given equation is approximately $\color{blue}{-1.769}$.
