What you should do is locate the next stud that is either 16" or 24" away. Then cut away all drywall from corner up to the edge of that stud. Attach nailer 2x2 pieces of wood to both that stud and the stud at the corner. You may then attach drywall to the nailers. Tape and finish. A step-by-step tutorial is given at http://www.drywallinfo.com/drywall-repair-videos.html
If this is an area that gets water splashed on it, you might use 1/2" Durock cement board instead of drywall as your patch piece. You can finish this like drywall. You will have to skim coat to fill in the Durock surface but it will work for you. I did this in our bathroom next to our tub 3 years ago and it has held up great. Before that, any repair I made was quickly wrecked by splashed water.