The back glass got broken today on my iPhone X and Won’t power on...

Hmmm…I know this is a technical forum but I think you also have another serious problem here that needs to be addressed. That is not acceptable behaviour in any circumstances and I hope you will be able to do something about this.

Now, let’s talk about the phone. The iPhone X is still under warranty although with the physical damage it sustained, Apple may not cover any repair under this warranty. I would try and bring it to the Apple store first to see what they can do. They will probably offer you an Out-of-Warranty replacement.

If you want to have this repaired by an independent shop, then the back glass and either/or (or both) the screen and a micro-soldering repair may be necessary. Unfortunately, there’s not enough information here to offer a solid diagnosis. This will cost less than an OOW replacement but it still won’t be cheap.

The iPhone X is more tricky to work on than an iPhone 6 from a DIY perspective and the replacement parts are expensive. That means you have to buy the parts up front to see if they will solve you’re problem or not. So start by going to Apple to see what they can do. You can also drop by an independent shop that is well reviewed to see what they suggest. Then you can decide what’s the best course of action or drop by here and let us know so we can give you more guidance.