Convert $ x^2 - y^2 -2x = 0$ to polar? So far I got
$$r^2(\cos^2{\phi} - \sin^2{\phi}) -2 r\cos{\phi} = 0$$
$$r^2 \cos{(2\phi)} -2 r \cos{\phi} = 0$$

You are on the right track.  Now divide through by $r \ne 0$ and get
$$r \cos{2 \phi} - 2 \cos{\phi} = 0$$
or 
$$r = 2 \frac{ \cos{\phi}}{\cos{2 \phi}}$$
