How do you edge a cut carpet
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Binding tape from the sewing department of your local big box store should work. If the carpeting is thick pile, you may need to remove some from the edge of the carpeting before adding the binding. If you use fabric glue to attach the binding (rather than only sewing), you should still add a few stitches at least at both sides of each corner and every foot or so to help hold the binding in place.
You can take it to a carpet place and have it bound. They do a great job and will match the color perfect. It will last forever. I've done many runners like that - and they are still good -
with a sharp carpenters knife
if your really tight on money i have seen people use fun printed duck tape it comes in all kind of nifty print. check out amazon or walmart