Interestingly, you can do this one logically just as well and as easily as Grigori's mathematical method (it is, in fact, the same thing, just in a different idiom):
The square root is defined as the number which, when multiplied by itself, gives the number in question (x in this problem). In most cases, the number in question will be a positive one. All positive numbers have two square roots, one positive and one negative. This is because multiplying a positive by a positive results in a positive and multiplying a negative by a negative results in a negative. Because the positivity/negativity of the roots, in a way doesn't matter, we can see that the absolute values of the two (that is, their value without regard to negativity/positivity) must be the same. Thus, they must reflect around zero, each being an equal distance away from zero. Thus, since we know the difference between the roots is 30, half of which is 15, we must therefore also know that the roots are going to be 15 and -15, so we can just go ahead and square that.