Selected Quarterly Financial Information (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Oct. 31, 2017	Jul. 31, 2017	Apr. 30, 2017	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Quarterly Financial Information Disclosure [Abstract]
Net revenue	$ 737.3	$ 660.9	$ 611.7	$ 559.9	$ 553.8	$ 515.3	$ 501.8	$ 485.7	$ 2,569.8	$ 2,056.6	$ 2,031.0
Gross profit	660.3	588.6	541.9	493.1	480.7	437.8	427.2	407.5	2,283.9	1,753.2	1,689.1
(Loss) income from operations	40.3	14.7	(24.7)	(55.3)	(181.9)	(100.0)	(107.6)	(119.6)	(25.0)	(509.1)	(499.6)
Provision for income taxes	(31.7)	(35.2)	(16.0)	(18.6)	24.8	(8.6)	(17.6)	(8.2)	(38.1)	(9.6)	(58.3)
Net (loss) income	$ 64.7	$ (23.7)	$ (39.4)	$ (82.4)	$ (173.5)	$ (119.8)	$ (144.0)	$ (129.6)	$ (80.8)	$ (566.9)	$ (582.1)
Basic net (loss) income per share (in dollars per share)	$ 0.30	$ (0.11)	$ (0.18)	$ (0.38)	$ (0.79)	$ (0.55)	$ (0.66)	$ (0.59)	$ (0.37)	$ (2.58)	$ (2.61)
Diluted net (loss) income per share (in dollars per share)	$ 0.29	$ (0.11)	$ (0.18)	$ (0.38)	$ (0.79)	$ (0.55)	$ (0.66)	$ (0.59)	$ (0.37)	$ (2.58)	$ (2.61)
(Loss) Income from operations includes the following items:
Stock-based compensation expense	$ 74.0	$ 64.2	$ 56.9	$ 54.4	$ 62.1	$ 65.1	$ 58.8	$ 59.0	$ 249.5	$ 245.0
Amortization of acquisition related intangibles	11.1	7.8	7.2	7.4	8.6	8.7	8.9	10.4	33.5	36.6
CEO transition costs	0.0	0.0	(0.1)	0.0	(0.2)	0.0	10.6	11.0	(0.1)	21.4
Acquisition related costs	11.9	1.8	2.5	0.0					16.2
Restructuring and other exit costs, net	$ 1.9	$ 3.7	$ 13.8	$ 22.5	$ 93.9	$ 0.0	$ 0.5	$ (0.3)	$ 41.9	$ 94.1	$ 80.5