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I am tired of losing games due to blindly hanging pieces and getting mated in a silly way

"rapid 5, blitz, bullet" is the answer you are seeking I think. you used 1.6 sec per move on average on the first game.
increasing speed of execution always increases errors.
You play too fast. It's better to play one long but quality game than a hundred short ones.
You first need to get accurate. Besides, if you're planning to get an over the board title you will have to play really long games, so build up patience. Some players like me will probably never play well in short games, but that's fine, because those do not matter anyway. I used to play long games against an engine. I would lose, but I would also learn something, so I kept doing that.
Part of my thought process (and others) that helps is asking: "What is the idea behind my opponents last move?". This should be the first thing you think of after every move. Naturally it's a lot easier to do this in longer games.

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