--------------------------------------------------------

--------------------------------------------------------

first take half the coefficient of x , that is half of (-18) =9
combine it with x to get (x-9)^2
now expand (x-9)^2 , you will see that 9^2 is a new term which
was not there in the original equation x^2 -18x +45 =0
so you will rewrite as (x-9)^2 +45 - 9^2 =0 ...
  answer and  some steps are given below

================
* *
================