cos(2x)−cos(x) = -((sin^2)x + 1/4)

Need help solving.

since sin^2 = 1-cos^2

and cos(2x) = 2cos^2 - 1,

2cos^2 - 1 - cos = -1+cos^2 - 1/4
cos^2 - cos + 1/4 = 0
(cos - 1/2)^2 = 0
cos = 1/2
x = pi/3 or 5pi/3