# Thread: How to solve for x

1. ## How to solve for x

Hello,

How do you solve for x? do you have to factor out cosine? how?

$-2cos(x)-2cos2(x) = 0$

Thanks!

2. $-2 \cos x -2 \cos(2x) = -2 \cos x - 2 (2 \cos^2x - 1) = -4 \cos^2 x - 2 \cos x + 2$ (this identity comes from your other post).

Hence
$-4 \cos^2 x - 2 \cos x + 2 = 0$

$2 \cos^2 x + \cos x - 1 = 0$

Set $z = \cos x$, then

$2z^2 + z - 1$.

Solve for z using the quadratic formula

3. Hello everyone
Originally Posted by icemanfan
... $2z^2 + z - 1$.

Solve for z using the quadratic formula
Or, better still, by factorising.