7750 with 350W PSU?

I would like to ask whether an Saphire HD 7750 will work with a 350W PSU. I am worried it might not work as it is set as a requirement 450W PSU. I would be really grateful if you could answer me.

Here is my system:
-Intel Dual Core Processor- 2x2.8
-RAM 4GB DDR3
-Motherboard MS-7529 (PCI-E 1.0)
-Power Suply 350W
-Windows 7

Here is a link to my power supply:
http://i705.photobucket.com/albums/ww60/crcf4/20120424_...