\(c = (\frac{b}{2})^2 \)
in completing the square what is the term called for using that to get the third term?
I really do not know what you are after. Maybe some info is missing?
but...
\(x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2\)
extracting coeffieceints?