Add Google as Default Search Provider for Windows 8.1 IE 11

Solution 1:

1. Click on the gear in the top right corner of IE.
2. Click on Manage add-ons
3. In Add-on Type select Search Providers
4. In the bottom of the window, click on Find more search providers ...
5. A new window will open, click on Google Search
   1. NOTE: If nothing happens after clicking Google Search press F12 and the Developer Tools will appear in the bottom of the window.
   2. Scroll to the bottom of the Developer Tools window and click on the monitor and smartphone icon, (the Emulation icon, you can also press Ctrl + 8).
   3. In the Mode section, change Document mode to 10.
   4. After the page reloads, click on Google Search
6. Click on Add to Internet Explorer
7. A pop up appears. Check Make this my default search provider.
8. Click on Add

And that's all, you are all set!!!

NOTE: Check comments for extra info