According to a document I am reading, I can approximate the square root of some real number $x$ via "Newton's method" by repeatedly taking $z = z - \frac{z^2 - x}{2z}$ after beginning with some random value $z$. This approximation seems pretty good.
However, according to Wikipedia, shouldn't this approximation be $z = z - \frac{z^2}{0.5z^{-0.5}}$ instead? Where did the above equation ($z = z - \frac{z^2 - x}{2z}$) come from?