Your teacher didn't pick the most simple way to do this problem, the steps your teacher gave is confusing. Using the same concept, I am going to do this my way then I will show a different method.
3x^2+24x+9=0
x^2+8x+3=0
x^2+8x+16+3=16
(x+4)^2=13
x+4=±
x=-4±
This is how you are suppose to solve it with completing the square and all the steps, to fill your teacher's blank you will have to go from my answer to how your teacher want you to write it.
*Now I am going to show you a way to solve this with the quadratic formula.
I am going to use the main formula because its more clear although the even formula is easier for this question.
3x^2+24x+9=0
x=(-24±
)/2*3
x=(-24±
)/6
x=(-24±
)/6
since 468 is a multiple of 36
x=(-24±6
)/6
x=-4±
This bottom way is really good if you can calculate quickly, with a lot of practice this way is much better for solving quadratic equations that cannot be factored.