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Stockholders' Equity (Common Stock Outstanding) (Details) - USD ($)
 1 Months Ended 3 Months Ended 6 Months Ended
Sep. 30, 2019
Feb. 28, 2021
Feb. 29, 2020
Feb. 28, 2021
Feb. 29, 2020
Common stock outstanding:          
Common stock outstanding, beginning balances (in shares)       150,330,358  
Common stock outstanding, ending balance (in shares)   149,366,501   149,366,501  
2020 Share Repurchase Program          
Common stock outstanding:          
Share repurchase program, amount authorized $ 600,000,000.0        
Capital allocation framework period 2 years        
Number of shares repurchased (in shares)       9,400,000  
Value of shares repurchased       $ 345,900,000  
Share repurchase program, remaining amount available   $ 254,100,000   $ 254,100,000  
Common stock:          
Common stock outstanding:          
Common stock outstanding, beginning balances (in shares) 153,520,380 150,471,570 152,300,356 150,330,358 153,520,380
Shares issued upon exercise of stock options (in shares)   0 43,069 0 56,999
Shares issued under employee stock purchase plan (in shares)   771,548 595,717 771,548 595,717
Vesting of restricted stock (in shares)   24,054 322,872 2,241,136 2,239,612
Purchases of treasury stock under employee stock plans (in shares)   (8,873) (86,706) (610,279) (617,123)
Treasury shares purchased (in shares)   (1,891,798) (1,767,782) (3,366,262) (4,388,059)
Common stock outstanding, ending balance (in shares)   149,366,501 151,407,526 149,366,501 151,407,526