Greetings

I currently have Windows 7 x86 installed on my computer. I want to install Windows 7 x64 on a different partition on my computer. However there is a little issue, I cannot run the x64 install from Windows 7 x86 which I currently have.

I was planning to Install Windows 7 x64 on another partition to then boot up from that partition to install it on the partition I actually want my OS on. Once that is complete I could just format the partition from the Windows 7 x64 that I didn't need anymore. But the installer will not run from the x86 version of Windows 7 even though I do not want to upgrade that Windows directly.

The reason I'm doing this in such a weird way is that my optical drive is broken and I'm really not into buying a new one since I would use it like once every year or so. I also don't have a USB Flash Drive which is big enough to hold the installation files.

As far as I'm aware I cannot use an external hard drive such as this one, which I do have. Are there any alternatives in which I can install Windows 7 x64 or am I forced into buying a USB Flash Drive or new optical drive?

Thank you in advance for your replies.

Edit:
This picture shows my current partitions on my laptop. I want to get Windows 7 x64 on the C partition but have to install it first on the F partition to then boot up the F partition windows to format C and install x64 on that one. My external drive is J.

Edit 2: No alternative computer which has a DVD drive, install files are located on an iso from MA3D. To install my 32 bit version I mounted the ISO in Daemon Tools to replace my Windows Vista but since I cannot run 64 bit into my 32 bit OS this doesn't work.