This is a cube, with an edge beveled:

[![enter image description here](https://i.stack.imgur.com/jL34I.png)](https://i.stack.imgur.com/jL34I.png)

I'm not sure how to deal with the 2 ngons left here. How can I make it all-quad topology while maintaining the shape? Manually cut them like this:

[![enter image description here](https://i.stack.imgur.com/a2K7C.png)](https://i.stack.imgur.com/a2K7C.png)

? But when there are a lot of segments it gets tedious quickly. Plus what if it's not a cube?

[![enter image description here](https://i.stack.imgur.com/d7ZIe.png)](https://i.stack.imgur.com/d7ZIe.png)

Is there a more general or automatic way to handle the ngons left by beveling?