$$\cos^2(2x) + \sin^4(x) = 2$$

So lost on how to solve these things and it's already midnight. 3 days I've spent reviewing and doing practice, but I can't find any proper information on how to go about this. 

I figured I would try and break $\cos^2(2x)$ down into $2\cos^2(x)$ but I can't determine if that was the way it was done? 

Edit: I am simply trying to figure out how to do this. I recall one of my professors explaining how to break cos^2(2x) down...