whoop, thunderstorm, gotta check out. =p I know I didn't help, but hey, at least you know it wasn't any more effort not to do it implicitly.
Edit: Well, that brushed off quickly. Anyway, all your asking is what your "domain" restrictions should be? You already established a relationship between x and y when you substituted for x^2 and unlike a lot of optimization problems, this one doesn't require to be answers along a certain interval.