HI;
I need to complete the square for 9x^2 + 12x + 4.
but I can't factor out the 9.
therefore how do I start?
You start by learning what a "perfect square" is! For any numbers, a and b, $(a+ b)^2=a^2+ 2ab+ b^2 $. The quadratic here is $9x^2+ 12x+ 4 $. Clearly, $a^2= x^2 $ and $b^2= 4$ so a= 3x and b= 2. From that 2ab= 2(3x)(2)= 12x. The whole point of "completing the square" is adding and subtracting that "2ab" part. I don't see how you can learn "completing the square" without first knowing what you want to get.