Broken drill bit is stuck in DeWalt drill

I have one of the cheaper Dewalt corded drills. It does have variable speed (according to how far in you press the trigger), but seems to not go as slow as my battery drill. It also does not have a clutch. I would never use it for screwing.

Put the drill in reverse, firmly grip the chuck (the part you were calling the head) and gently squeeze the trigger up the point that you cannot hold on. If you hear clicking, and it doesn't torque very much, you need to turn the torque setting up to the maximum (the highest number, or the drill setting if it has one). If it still doesn't budge and you're not able to hold the chuck against the force of the drill, you may want to use something stronger than your hand to hold the chuck. A strap wrench is well designed for this task and won't damage the chuck.