x^2 + bx + c == [x + sqrt(c)]^2
x^2 + bx + c == x^2 + 2*x*sqrt(c) + c
bx = 2x*sqrt(c)
x != 0 // simplifies uselessly to c == sqrt(c)
b = 2*sqrt(c)
2*sqrt(c) = b
4c = b^2
c = 0.25 * b^2
Add onefourth the square of b to a binomial of the form (x^2 + bx) to transform it into a perfect square trinomial.
(Damn, I need to get back to that Sine of One Degree thing, I left all those 60+ sheets of inkstained paper filled with my work on that back at DE xD)
