Calculate x from x^3+3=x^2

We'll use numerical methods to find the solution. Graphing  and  together shows that there is only one point of intersection - slightly less than -1. So we know that there is only 1 real solution. 
We use Newton's method: 
 
 

then 
 
We wont bother simplifying because we'll do the calculations by calculator: 
guess x=-1