Question in relation to completing the square In description of "completing the square" at http://www.purplemath.com/modules/sqrquad.htm the following is given : 

I'm having difficulty understanding the third part of the transformation.
Where is
$ -\frac{1}{4}$ derived from $-\frac{1}{2}$ ?
Why is $ -\frac {1}{4}$ squared to obtain $ \frac {1}{16}$ ?

If you have $(a+b)^2 = a^2 + 2ab + b^2$ and $a^2 = x^2, 2ab = -x/2$, then $a=x, b = -1/4$.
$1/16$ is $b^2$ which is needed to form $a^2 + 2ab + b^2$ in the LHS and move remain elements in the RHS.
