Rewrite it as $\displaystyle \displaystyle 2 + \cos{(x)} = 2\left[ 1 - \cos^2{(x)} \right]$, expand everything, move to one side and solve the resulting quadratic equation.
Generally, trigonometric equations with powers are only possible to be solved if you can get it the equation to be only of a single trigonometric function (in this case, the cosine function).