co-ax repair

Ok, i started getting bad reception on my FM stations in my car (aftermarket radio), so i went straight to the antenna wire. When i pulled it out of the back of the radio, the end fell off. I think i know a way to fix this,but am not sure if there is an "appropriate" way to do so. Anyone know how to do this?

I can't say that I have ever fixed one (guess I have never broke one)

Ya, i never have either. I've got another antenna cable, im thinking of just cutting that one and stripping the insulation over the shield and then from the core on the inside and just soldering them together. then some tape or wrap or something