You're using the convention ds^2 = dt^2 - dx^2. So if you get ds^2 > 0, this means that the time part, dt^2, of your equation dominates, making the separation 'time-like'. On the otherhand, if ds^2 < 0, then your space part, dx^2, would dominate making the separation 'space-like.' (You weren't getting them mixed up in your solutions).

As a side note, you need to be careful of which convention you're working in. Some texts use ds^2 = -dt^2 + ds^2, which means ds^2 < 0 is timelike. The property of the separation doesn't change, just which regimes you choose to call negative and positive.