$2\cos{x} - \cos{}2x = \dfrac{5}{4}$
Find all values for $x$ in the interval [$0$°, $360$°]
Going from this equation I arrived at (by way of quadratic addition)
$\cos{x} = \dfrac{1+\sqrt{2}}{2\sqrt{2}}$
which I translated to
$x = 31.3997$° (approximately)
However, there are three other solutions ($328$°, $81$° and $278$°, all with fractions after the decimal point). How do I find these values, and more generally, how do I find all possible values for $x$ between $0$° and $360$°?