Hey Paul - get yourself a scrap piece of drywall the same thickness as what you have.
Cut a hole about 1" larger than the hole in your wall. Then cut the gypsum - but not the paper - from the patch.
What this should look like is a smaller drywall circle with just the paper around it approximately 1". This should fit into the hole in your wall - and the paper around it will hold it there.
Patch with drywall mud - once that's dry - sand - don't forget to prime (or you could get a flash) and repaint.....
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