Solving a trigonometric equation

[KiwiKid]

Homework Statement

Solve 2cos(x)^2 + 3cos(x) + 1 = 0 for 0 <= x <= 2pi

Homework Equations

Trigonometric equations, yadda yadda yadda.

The Attempt at a Solution

2cos(x)^2 + 3cos(x) + 1 = 0
cos(x)(2cos(x) + 3) = -1
cos(x) = -1/(2cos(x) + 3)

I then figured out that you get a solution when cos(x) = -1 (so x = pi). However, there are supposed to be multiple solutions, and I don't know how to find these. Any pointers?

 

[SteamKing]

Notice that the original equation is a quadratic in cos(x).

 

[KiwiKid]

Notice that the original equation is a quadratic in cos(x).

Ah, found it. I've been messing around with trigonometric identities for half an hour now. Turns out I just had to factor the whole equation. Thanks. =D