When I was a wet-behind-the-ears engineer, stuffed with all sorts of exact solutions to carefully chosen problems, I thought that it was my job to find an exact solution to every problem that came my way.
Boy, I wasted a whole bunch of time on that.
Now I understand that you just need to approximate things well enough that the error from the approximation is lost in the noise of the error from everything that I don't and can't know, and to make things adjustable so that I can fix them after they're all built and pretty.
It's still fun to solve things like catenary curves, though.