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Chris Wilder's side are 10 points from safety with just three games left following their 25th league defeat of a dismal season. The bottom of the table Blades, who have only three league victories this term, will return to the Championship just after 12 months.
Anel Ahmedhodzic put the visitors ahead at St James' Park, but Alexander Isak struck twice, Bruno Guimaraes and Callum Wilson each netted and Ben Osborn scored an own goal to complete the rout.
It was the Blades' fourth successive defeat, leaving them without a win in their last 11 games.
They have set a new record for the most goals conceded in a 38-game Premier League season, with 97 allowed in 35 games. They are also on track to beat Swindon's all-time Premier League record of 100 goals conceded in 1993-94 when the division was made up of 22 teams not current 20.
