Easiest way is to use something like this. Then use some spackle over it, let dry, then paint. Just follow instructions, it's not too difficult. Good luck.

Edit: your wall is very smooth, so its going to be a challenge to get it to look just right without rubbing it all the way to the wire. Do your best and know that even if it isn't perfect, most people won't notice small discrepancies.

If you want to use your pieces of drywall, you would have to make the hole bigger...you don't want to do that.