cos 2x = cos x

Well first thing I would have to do is convert this into a quadratic formula (meaning ax^{2}+bx+c)

Though, my teacher helped me get started, and told me to do this:

2cos^{2}(x)-cos(x)-1

I was lost at how the cos 2(x) became 2cos^{2}x

Can anyone explain to me this?

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Though, after that I would factor it then find the x's from there.