Complete The Square:

(Z^2) - 19z=66

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