i would like to know how you derive the alternative quadratic formula from ax^2+bx+c=0. i know how to derive the quadratic formula but not the alternate.

ax^2+bx+c

ax^2=(-)bx-c

ax^2=(-1)b(x+c/b)

ax^2/b=(-)x-c/b

(ax^2/b)+x=(-)c/b

x(ax/b+1)=(-)c/b

x=(-)(c/b)(ax/b+1)

x=(-)cax/b^2+b)

(-)x^2=ca/(b^2+b)=x^2

x=±sqrt(ca/(b^2+b))

I think that is what you are looking for. Someone double check my math though.