Html. Putting Two Inputs Fields Togehter?

I was developing a site search for someone and I got it fully functioning-- the php calls on the input field with #searchField.All the user has to do is begin typing and the results appear underneath without ever having to click submit or enter/return.However, the customer was wondering if I could integrate the Wolfram Alpha Computational Search as well.So that a page visitor or user would type in the search field the results searching his site would appear below, as mentioned above; but, if one typed a query and hit enter then it would search WolframAlpha.I first made a page, here, that uses the code Wolfram Alpha's developer community was giving to developers that creates an input field and searches wolfram Alpha one hits enter. (It writes the necessary html in a messy way and includes this base.css file)Here is a screenshot of the html code that the wolframAlpha.js file writes from chrome dev tools.

After doing so, I put the code of the page I developed for my client and the above page together and what I got was two separate input fields, one that searches the site (top, but it doesn't work due because I did not attach that file as where this is located can't parse PHP) and one that searches wolfram alpha (bottom -- does work).You can see the result of the combined code here.