Put a drop cloth against the bulging wall.
Put on safety glasses and drill four holes into the wall, each about 2 to 3 inches outside each "corner" of the bulge.
Insert a reciprocating saw into one of the four holes and cut out a square, cutting the entire bulge out of the wall. Discard the cut piece from the wall.
Measure the size of the square hole cut out of the wall. Then measure and mark a drywall panel to cut out a like-sized square. Use a circular saw to cut a square "patch" for the hole in the wall.
Insert the square patch into the hole in the wall and fasten to the exposed studs with drywall screws using a screw gun.
Stick drywall tape around the edges of the patch, then cover the patch and the tape with joint compound using a putty knife. Let sit overnight to dry.
Sand the patch with sandpaper, then apply a coat of primer. Allow the primer to dry as long as recommended by the manufacturer, then paint over the patch with a roller using the same color paint that is on the rest of the wall.