Find the range of $f(x)=11\cos^2x+3\sin^2x+6\sin x\cos x+5$ I'm trying to solve this problem.

Find the range of $f(x)=11\cos^2x+3\sin^2x+6\sin x\cos x+5$

I have simplified this problem to $$f(x)= 8\cos^2x+6\sin x\cos x+8$$ and tried working with $g(x)= 8\cos^2x+6\sin x\cos x$.
I factored out the $2\cos x$ and rewrote the other factor as a linear combination of cosine.
It reduces down to $$g(x)=10\cos x\cos\left(x-\tan^{-1}\frac{3}{4}\right)$$
But then I'm stuck here. Please help me. Perhaps there's a different way to approach this?

$$f(x)=8\left(\frac{1+\cos {2x}}{2}\right) +3\sin {2x}+8$$
$$f(x)=4\cos {2x}+3\sin {2x} +12$$ 
The range of $$4\cos {2x}+3\sin {2x}$$ is $[-5,5]$
Hence maximum and minimum values of expression are $17$ and $7$ respectively. 
