Write 4x^2+18x+2 in form a(x+m)+n.

First thing I like to do with questions like these is to check if I can simplify the expression given, and we can simplify this expression. So 4x^2+18x+2 can be simplified to 2x^2+9+1. The next step for me is to take out a 2, this will turn the bracket into 2(x^2+9/2+1/2), and then use the completing the square method for inside the bracket. This transforms the expression to 2[(x+9/4)^2-81/16 +1/2]=2[(x+9/4)^2-73/16]. We will then expand out the bracket, this turns the expression to 2(x+9/4)^2-73/8. This is the answer to the question, a=2,m=9/4 and n=-73/8.