In facsimile, a frequency modulationsystem where one frequency represents picture black and another frequency represents picture white[?]. Frequencies between these two limits may represent shades of gray
An intentional frequency change used for modulation purposes
... will make it a perfect square trinomial of the form x2 + 2xy + y2. Since "2xy" in this case is (b/a)x, we must have y = b/(2a), so we add the square of b/(2a) to both ...