A small hack to the search box?

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It did not become apparent to me after many visits to the site that once I type in something into the search box and the results aren't what I want, I can press the "Ask Your Question" button next to the box to convert my search query to a question.

I feel the "Ask Your Question" button and the search box feel disconnected. How about a small hack that will prompt the user as a drop down from the search box to "Ask this as your Question" or probably grouping together the searchbox, X, search icon and "Ask Your Question" button?