Would it shock you if I told you that the way to start is todo what they tell you to do? Replace both and in the formula by x.

That gives you solve that for x.

IF this sequence converges, then and each of those limits is of the same sequence and so is equal to x. This is, by the way, a well known iterative method for finding square roots. In fact, it is often known as the "Babylonian method"!

Methods of computing square roots - Wikipedia, the free encyclopedia