Answer
The two solutions in the given interval are:
$x = 0$
$x = 0.3760$
Work Step by Step
$x^3-cos^2~x = \frac{x}{2}-1$
$cos^2~x = x^3-\frac{x}{2}+1$
We can graph the two equations $~~y = cos^2~x~~$ and $~~y = x^3-\frac{x}{2}+1~~$ to find the points of intersection.
The blue graph is $~~y = x^3-\frac{x}{2}+1$
The red graph is $~~y = cos^2~x$
We can see that the points of intersection occur when $~~x = 0~~$ and $~~x = 0.3760$
The two solutions in the given interval are:
$x = 0$
$x = 0.3760$
