I think you may be thinking a little too hard about things as the writer. Instead look at things from your characters' perspectives. Unless you're writing an engineer or someone actually building X, they probably won't actually know how it works. Heck, even an engineer building X would only know about the tiny portion they actually work on. The rest is probably done by other teams or even other computers.
Remember that to the layman, things just work.
Let's imagine that X is actually a car in today's world. If you were to ask <PERSON> on the street, he'd explain to you that the car works by turning the keys and pressing the right pedals. 627
He probably understands what it's good for and how it interacts with the world (ie: what can go wrong if you collide with something). He knows that when the little needle gets close to the 'E' he needs to put more Magic Fluid in it from one of the Magic Fluid depots around the city. But that's about it.
Focus on the things your characters care about. Those are the things that will affect them
Does <PERSON> know how the car burns the gas to cause propulsion? Or how the brakes work? Or even why it's so easy to turn a wheel and change the direction of two tons of metal? I'd guess not. And guess what--this lack of knowledge doesn't even affect him!
What <PERSON> does care about is how the price of Magic Fluid has been going up lately. He cares about how cool the new models of cars look compared to his old one or what (to someone unfamiliar with the concept of cars) minor features were added.
You're not writing an encyclopedia or manual--you're writing a story!
If knowing or not knowing a fact doesn't affect your characters, then guess what--it doesn't affect your story! And if it doesn't affect your story, then it has no place in the pages you're writing.
Remember that all of this technology is just a pile of tools that work to build an image for the reader of what your world is like and propel your story. At the end of the day, all that really matters for the story is probably exactly what you've written: it's "see[ing] the technology in use, understand[ing] what it does, and even what it requires to work." 805