Is any number exactly 2 less than its cube?
This is what I did:
$\displaystyle x=x^3 - 2$. I graphed the equation and came up with x = 1.521. Is this correct?
No. The number you've found is not EXACTLY 2 less than its cube.
The question as stated requires you to establish the existence (or otherwise) of such a number, not to actually find the number. Existence is simple to prove since every cubic equation has at least one real root ....