Radeon 7870 on a Dell 460W PSU

I want a card that can handle BF3 and TW2 on high or ultra at my monitors' native (1920x1080), and a 7870 looks like the the cheapest card that can do it. The issue is I've looked at multiple psu calc's and threads and there's a wild range of opinion on whether a Dell 460W PSU can handle that card. Can I get a definitive answer on this? If yes, I was pulling for a Sapphire.

Current Specs:
Dell XPS 8500
LGA1155 Core-i7 3770 3.4 GHz
2TB 7200 RPM HD
1GB Geforce 640 gddr5
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More about radeon 7870 dell 460w
  1. For a system using a single Radeon HD 7870 graphics card AMD specifies a minimum of a 500 Watt or greater power supply. The power supply should also have a combined +12 Volt continuous current rating of 28 Amps or greater and have at least two 6-pin PCI Express supplementary power connectors.

    Total Power Supply Wattage is NOT the crucial factor in power supply selection!!! Total Combined Continuous Power/Current Available on the +12V Rail(s) @ 50°C ambient temperature, is the most important factor.

    The Dell XPS 8500 460W power supply, with its combined +12 Volt continuous current rating of 32 Amps and with two (6+2)-pin PCI Express supplementary power connectors, is sufficient to power your system configuration with a single Radeon HD 7870.
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