Go here to download the X86 version of Windows 7 Home Premium:
32-bit Windows 7 Home Premium x86 ISO
http://msft-dnl.digitalrivercontent..../X15-65732.iso
Save the ISO image file and then burn it to a good quality blank DVD with ImgBurn (it's free and easy to use).
www.imgburn.com
Burn at no faster than an 8X burning speed and then use ImgBurn's Verify Feature to ensure the burn went well. Then you're free to install the Home Premium X86 version. Your same product code key will work.
You'll only be able to access 3.25 GB of the 4 GB of RAM on your laptop because of the limitation in the X86 operating system.
BE SURE to download all the correct 32-bit drivers for Windows 7 from your laptop maker's website for your model of laptop and store them on a flash thumb drive, external hard drive or burn to a CD-RW rewritable disc.
BTW, that's sweet looking laptop you have there... now I'm covetous. LOL!
Let us know how it goes... also be sure to install the mobile chipset drivers first before any others and then the video driver. LAN driver, etc.
Go to this Samsung link for your drivers, you'll notice that some drivers are both 32 & 64-bit drivers while others are bit specific:
http://www.samsung.com/us/support/downloads/NP-R780E