((a)t-u)^2 + 2u(t-u) =t^2 -u^2

After converting the original quadratic equation (ax^2 +bx+c= 0) into

x^2 + (b/a)x= -(c/a)introduce the auxilliary variablestandu, wherex=t-u. Then, using, find(a)tandu(and ultimatelyx) in terms ofa,b, andc.