help me people

My math teacher sent me some homework via EMAIL at YESTERDAY MIDNIGHT. And he wrote that me and another student has to solve all the tasks, or else we will be given enough grades to fail at the end of this term. ISN'T HE CRAZY???

So please, my fellows, help me shove the answers up his ass.
Here is the first i couldn't solve.

x^2 + 32x + 2264 = p^2; p is a prime of choice
find x, if x is an integer

tl;dr: please give tips how to solve the problem above

>>10
Not to mention that it's 5000% too easy for the putnam.

(If I hadn't blanked on A2 and B2 I would've gotten nine and coulda fukken won that cocksucker this year >:( .  I bet I'll be the only idiot with an honorable mention who DIDN'T get A2.  )