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How to clean vomit from carpet with baking soda
Remove residual puke from the carpet.
Probably the worst but an extremely important step.
Suit up with rubber gloves (and possibly any other protective gear you feel is necessary).
Remove as much vomit from the carpet with paper towels and immediately dispose in a plastic trash bag. Consider holding your nose during this process if you sensitive to smell or you can spray concentrated room spray in the area to reduce the bad odor.