f(x)=x^2+6x+3
seperate x terms
f(x)=(x^2+6x)+3
take 1/2 of 6 and square it
6/2=3
3^2=9
add negative and positive inside parenthasees
f(x)=(x^2+6x+9-9)+3
factor perfect square
f(x)=((x+3)^2-9)+3
get rid of parenthasees
f(x)=(x+3)^2-9+3
f(x)=(x+3)^2-6
last one is answer
