I think this is nice. It's a method of calculation derived from an important fact—that quadratic equations have two solutions and those solutions can be written in such a form.

I don't have the experience or interest to debate whether it's better or worse than any other method pedagogically. I can definitely imagine that I would have appreciated learning this method as well as completing the square as a child.

But honestly, the real interesting thing here is the (a) gathering information about what you think the solution ought to look like and (b) working backwards from there. That's a good general trick and worth having in your back pocket. It also emphasizes the importance of visualizing and examining your belief about what should occur.

People should suspect the fundamental theorem of algebra long before they prove it.