To solve the equation using complete square method we proceed:
z^2-19z=66
but
c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4
(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3