write the general solution to 2cos^2x+cos x=1

Answer 1

it factors...

2cos^2x + cosx - 1 = 0
(2cosx - 1)(cosx + 1) = 0
cosx = 1/2 or cosx = -1
x = 60° or 300° or x = 180°

general solution..... add 360k° to each answer

I will leave it up to you to change the above to radians if you have to.

Answer 2

Treat cosx as a new variable u, and solve the resulting quadratic equation for u.
2 u^2 +u -1 = 0
(2u -1)(u + 1) = u
u = cos x = -1 or 1/2

Now solve for x. One answer is pi radians. Another is pi/3. There is another, in the fourth quadrant.