Thanks Tav uhmmmm how about this though:

These are two different circles. One has a fixed radius of 50, the other I have to determine based on some other criteria that isn't relevant at this point. I should have been more clear that I need to find the x-values of the points where the two circles intercept! From what I understand, I have to substitute my solved y value into the other equation, giving me...

x² + (sqrt(-x²+2500)+50)² = r²

and now solve for x... Ew.