The root volume cannot easily be extended in this layout. There's no free space after this partition, and LVM isn't being used either. Some fairly significant surgery would be needed no matter what. Possibly the easiest would be to boot from a livecd, create a new partition out of the 32GiB free space, and then use dd with a 1M block size to copy the existing root to the new root; and then wipe the signature on the old root. You'd need to check both /etc/fstab and grub.cfg to make sure it's looking for root with UUID rather than device. The UUID would be the same with this method, but the device will have changed. It's important to wipe the old signature to avoid having two identical filesystem volumes with the same UUID visible; not all file systems will tolerate this gracefully.