Credit to Hans De Goede (https://bugs.launchpad.net/ubuntu/+source/linux/+bug/1314198/comments/31)
This should enable the mouse to work as a normal touchpad mouse, so no multi-touch.
You need to add a Kernel Boot Parameter to set the flag
psmouse.proto=bare which will enable PS/2 Mouse Emulation mode on your touchpad.
To do this you can edit your default grub file.
sudo nano /etc/default/grub
Find the line that mentions
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" (or something similar) and add the flag to the end of the quoted string.
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash psmouse.proto=bare"
Then save the file and run a grub update.
Then restart the system and (hopefully) enjoy your new touchpad in PS/2 Emulation Mode.
This is a temporary fix as Hans De Goede mentions, this isn't a trivial fix. If I'm reading the situation correctly, support for the software that handled the touchpad used in the ASUS 550 range (and some other models) was deprecated in 14.04 and a suitable replacement hasn't yet been developed. So for now we don't get multi-touch in 14.04.
Having struggled with this for a while and finding nothing but launchpad bug reports, I'm pretty happy to finally have a working touchpad even if it doesn't have multi-touch!