merging two features from the same shapefile

I have a shapefile with all the roads in my county. Unfortunately, they are in segments. I am trying to combine them all into the same shapefile where each road has one continuous segment instead of hundreds of little segments.

I thought about using a loop, SearchCursor, selectByAttribute, and unSplitLine, but that is going to put them all into separate shapefiles (or continuously overwrite them). I need them all in the same shapefile so I can run my analysis on them.

Any thoughts about how I can move forward are appreciated.

Thanks,

Bryce