JQuery :: Submit Form - Clearing Text Fields

I am using jQuery AJAX to submit a form. When the data has been validated successfully and processed, I want to clear the form, but I am unsure how. I have been trying to make it work for a few hours now.

I am showing status messages in the container below:

When everything was successful, it looks like this:

And here is the simple code I use to clear the text fields:

What I need is a way to check if everything was successful and if so, then run the code above. I tried to do it in a few ways, but it kept clearing regardless of the status.