It is likely that a large portion of your battery problem is due to your graphics card (which is an optimus card). This means that it is designed to be turned on and off as needed. By default, in Linux I think it will run all the time and will not actually do anything for you. There are three options to remedy this:
1. Go into the BIOS and turn the video card off and use the integrated graphics.
2. Go into the BIOS and set the computer to always use the NVIDIA card. Ubuntu might recognize the card after this and offer to install drivers. I have not tested this. NOTE: This will not help the battery issue, but It might let you use the NVIDIA card.
3. Use http://bumblebee-project.org. This will allow you to launch an application and tell it to use the NVIDIA card. This way the video card will remain off until you specifically enable it for an individual application. If you do this then please note that it may break your system, however, I just talked someone through how to fix the system after this happens so It can be undone (at least in his case). There seems to be some confusions as to how to install bumblebee so I will include instructions below:
sudo add-apt-repository ppa:bumblebee/stable
sudo apt-get update
sudo apt-get install linux-headers-generic
sudo apt-get install bumblebee bumblebee-nvidia