#### Answer

$x = 1.28$

#### Work Step by Step

$2sin~2x-x^3+1 = 0$
$2sin~2x = x^3-1$
We can graph the two equations $~~y = 2sin~2x~~$ and $~~y = x^3-1~~$ to find the points of intersection.
The blue graph is $~~y = x^3-1~~$
The red graph is $~~y = 2sin~2x~~$
On the interval $[0,2\pi]$, we can see that the point of intersection occurs when $~~x = 1.28~~$
The solution over the given interval is:
$x = 1.28$