History of Hindu Mathematics: A Source Book v2.c17.s17.t2.13

v2.c17.s17.t2.13

Put $ax+½b=z,$ @(2.1) and then complete the square on the right-hand side. Thus the given equation is finally reduced to $aa'z² - β = w²,$ @(2.2) where $w = aa'y + ½ab',$ @(2.3) and $β = a²a'c' + (¼b² - ac)aa' - (½ab')².$