Fair Value Measures - Carrying Value and Estimated Carrying Value and Fair Value of Financial Instruments (Details) - USD ($) $ in Thousands	Feb. 28, 2023	Aug. 31, 2022
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total unamortized discounts and debt issuance costs	$ (14,391)	$ (17,576)
Total net carrying value of debt	1,735,609	1,982,424
Principal Amount
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	1,750,000	2,000,000
Principal Amount | Level 1 | Senior Notes | 2027 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	500,000	500,000
Principal Amount | Level 1 | Senior Notes | 2032 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	500,000	500,000
Principal Amount | Level 3 | Line of Credit | 2022 Credit Agreement | Term Loan
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	500,000	750,000
Principal Amount | Level 3 | Line of Credit | 2022 Credit Agreement | Revolving Credit Facility
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	250,000	250,000
Estimated Fair Value
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	1,631,738	1,908,780
Estimated Fair Value | Level 1 | Senior Notes | 2027 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	460,470	470,525
Estimated Fair Value | Level 1 | Senior Notes | 2032 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	419,705	438,205
Estimated Fair Value | Level 3 | Line of Credit | 2022 Credit Agreement | Term Loan
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	503,125	750,975
Estimated Fair Value | Level 3 | Line of Credit | 2022 Credit Agreement | Revolving Credit Facility
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	$ 248,438	$ 249,075