Carpet Repair Question

I have a commercial style carpet in my basement over a concrete floor with felt padding. While exercising this morning, I dropped a 25 pound iron barbell plate which landed in such a way that it caused a 3 inch long severe indentation in the carpet about 5 feet away from the wall. There appears to be a clean tear completely through the carpet and backing and it feels like there is now a hole or chip in the concrete floor underneath. I'm thinking of pulling the carpet back to where the hole is, repairing the hole in the concrete, and gluing some kind of patch to the backside of the carpet. Does anyone have any other suggestions? Can I use a clothes iron to apply the patch? Will the carpet need to be restretched when I lay it back down?
Thanks, Tillio

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