Answer
The two solutions over the given interval are:
$x = 0.6806$
$x = 1.4159$
Work Step by Step
$x^2+sin~x-x^3-cos~x = 0$
$sin~x-cos~x = x^3-x^2$
We can graph the two equations $~~y = sin~x-cos~x~~$ and $~~y = x^3-x^2~~$ to find the points of intersection.
The blue graph is $~~y = x^3-x^2~~$
The red graph is $~~y = sin~x-cos~x~~$
We can see that the points of intersection occur when $~~x = 0.6806~~$ and $~~x = 1.4159$
The two solutions over the given interval are:
$x = 0.6806$
$x = 1.4159$
