Now is not a great time to learn this:
When you cut the hole, bevel the cuts toward the center of the piece. One of the multitools does this extraordinarily well. With care, you can keep the original piece without damaging it. An application of DAP or similar will "glue" the piece back into the hole. A bit of touch up paint, but if the wall is white to off white, may not need any.
Another good trick is to cut the patch 4" larger than the hole. Cut the back side of the rock to size to fit the hole, peel off the drywall leaving a 2" flap of finish paper around the perimeter. Scrape back the texture around the hole, butter well with compound, install the plug, striking the paper tight to the wall. This will be much tighter than the build up you will get by taping and bedding on top of the drywall.
Neither system requires any fasteners and make quite sound repairs.