Verified answer

To complete the square in quadratic function y = x^2 + bx + c

just add and subtract (b/2)^2

Then here we must add and subtract 25a^2/4

x^2 -5ax + 25a^2/4 -25a^2/4 + b = (x-5a/2)^2 -25a^2/4 + b OK!

x^2 - 5ax + b =

x^2 - 5ax + (5a/2)^2 - (5a/2)^2 + b =

(x - 5a/2)^2 - 25a^2/4 + b