when you complete the square you have to focus on the coefficient for x (not x^{2}, just the regular x)
in your case its its 6 --> what you want to do is cut it in half (3) and then square it, thats where the
9 comes from.
ideally, you would have x^{2} + 6x + 9, but it has to be +116 at the end instead b/c thats just what your question is
so lets be creative and split the 116 into 9 and 107 ---> you have to do this b/c it has to total 116 and you want to have that 9 in there
x2 + 6x + 9 + 107
you can factor out the orange part into (x+3)^{2}
so its
(x+3)^{2} +107 so a is 3 and b is 107