Walls and Ceilings - How to fix this drywall mistake?

My brother misaligned the hole for a receptacle when we were hanging a sheet of drywall in the garage. It was just barely on top of the box, he didn't notice so when he drove in a few screws it broke the rock the width of the box and about and inch above the box and pushed it out maybe 1/16". We trimmed off the spot that was too low and it lined back up pretty good, but you can still see that it's broken. I drove in a screw right by it to see if I get it to stabilize and put mud over it, but it made it look worse.

What's the "correct" way to fix this? On one hand I think, "it's just a garage and it doesn't look *that* bad," but on the other hand I'd like to make it right.

There are two basic ways to repair it. If the rock is in good shape all you need to do is mud all the way around it to make it smooth. If there are cracks that need repairing they should probably be taped. Sometimes I'll take a square of construction paper, cut out the hole for the box and mud it in.

There are two basic ways to repair it. If the rock is in good shape all you need to do is mud all the way around it to make it smooth. If there are cracks that need repairing they should probably be taped. Sometimes I'll take a square of construction paper, cut out the hole for the box and mud it in.
So even though the rock is no longer "solid" I can just mud over it? I was thinking of that, but was afraid that I'd bump it sometime and the mud would crack in the outline of the break...

As long as the paper is intact or taped over it shouldn't be a problem.

When I mess up like that... I prefer to use a hard setting patch compound such as Durabond Water Putty. It dries much harder than joint compound and won't crack if you accidently bump it