Re deriving formulas for the quadratic eq.

\({\Large x^2+ax+b=0\quad|\quad a=2s\\ \Large x^2+2sx+s^2=s^2-b\\ \Large {\left({x+s}\right)}^2=s^2-b}\)

\({\Large x+s=\sqrt{s^2-b}\\ \Large x=-s±\sqrt{s^2-b}\quad|\quad s=\frac a2\\ \Large x=-\frac a2±\sqrt{{\left({\frac a2}\right)}^2-b}}\)

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[Eop]