I have a new bicycle that I have only ridden about 50 miles, and the front tube exploded one afternoon while the bicycle was in the garage. The explosion left a one inch long tear in the tube and it also tore a small piece of the side of the tire. The bead was okay, though. I (foolishly maybe) patched the tube and put it back on the wheel with the same tire. Then, I inflated to 20 psi, checked to make sure that everything looked okay, deflated the tire, and began inflating it to 100 psi. Around 80 psi, the tube exploded again exactly where the tire was damaged.
So my question is: does the tire look or sound like it needs replacement? I attached a picture of it.
Also, why would the tube randomly pop one afternoon when I was not riding it?