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Goodwill (Schedule of Goodwill Activity) (Details) - USD ($)
$ in Millions
6 Months Ended
Mar. 31, 2019
Sep. 30, 2018
Goodwill [Roll Forward]    
Goodwill $ 2,205.7 $ 2,211.1
Accumulated impairment losses (472.8) (472.8)
Goodwill, net 1,732.9 1,738.3
Currency translation effect (5.4)  
Patient Support Systems [Member]    
Goodwill [Roll Forward]    
Goodwill 543.4 544.4
Accumulated impairment losses (472.8) (472.8)
Goodwill, net 70.6 71.6
Currency translation effect (1.0)  
Front Line Care [Member]    
Goodwill [Roll Forward]    
Goodwill 1,368.0 1,370.6
Accumulated impairment losses 0.0 0.0
Goodwill, net 1,368.0 1,370.6
Currency translation effect (2.6)  
Surgical Solutions [Member]    
Goodwill [Roll Forward]    
Goodwill 294.3 296.1
Accumulated impairment losses 0.0 0.0
Goodwill, net 294.3 $ 296.1
Currency translation effect $ (1.8)