VGA Computer HDMI Monitor (In urgent need of help)

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I received a beautiful 24 inch ultrasharp monitor for Christmas this year and something unfortunate has appeared. I have an Alienware x51 r2, which does not have any hdmi ports, atleast what I can see, it has no hdmi ports. The cables that came with the monitor do not seem to fit my computer. I've tried various vga to hdmi convertors, but none of them seem to be able to connect to these cables. I need help. Someone out there. Please tell me if this is a lost cause.

 

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the dell specs manual says you do have a hdmi port. http/downloads.dell.com/manuals/all-products/esuprt_desktop/esuprt_alienware_dsk/alienware-x51-r2_reference%20guide_en-us.pdf