The case is swollen
the battery is swollen
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@letcherross time to take it apart and to replace the battery. You do not want to continue to charge your battery. That can make a bad situation worse. Use the Dell XPS 13 Service Manual to replace it. Page 16 will tell you how to accomplish the task. Discard the old battery properly. Don't just toss it in the bin. Check with your local environmental agencies on how to properly discard it.
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You will need to remove the battery and replace it.
Exactly what model is your DELL XPS 13 Series laptop?
crwdns2934271:0crwdnd2934271:0 mike crwdne2934271:0