You don't have to actually install the CD drive. Just open the case and connect the power and cable, then do the install. Just put a piece of cardboard or something under the cd drive so it doesn't touch metal to metal. It doesn't matter what kind of CD drive it is. Except maybe a USB connected, then it probably wouldn't work.
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If your equation requires either a complex combination of variables to get the desired result OR you can't seem to get the result regardless of the variables....it ain't your variables, it's your constant.