Find the zeroes of ax2 bx y c by completing the square So

Find the zeroes of ax^2 + bx = y - c by completing the square.

Solution

ax^2 + bx -y + c =0

a( x^2 +bx/a) + c -y =0

a(x +b/2a)^2 - a(b^2/4a^2) +c-y =0

a(x +b/2a)^2 - b^2/4a + c - y =0

a(x +b/2a)^2 = b^2/4a +y - c

(x +b/2a)^2 = b^2/4a^2 +y/a - c/a

x +b/2a = +/- sqrt(b^2 + 4a -4c)/2a

x = -b/2a +/- sqrt(b^2 + 4a -4c)/2a

x = ( -b +/- sqrt(b^2 + 4a -4c) )/2a