Posted Dec 5, 2019; updated Dec 29, 2019
I've recently been thinking about how to explain school math concepts in more thoughtful and interesting ways, while creating my Daily Challenge lessons. One night in September, while brainstorming different ways to think about the quadratic formula, I came up with a simple way to solve quadratic equations that I had never seen before. I was very surprised, as this method was easier to understand than what is typically written in textbooks. Adding this technique as a standard method would directly improve the learning experience for anyone trying to understand this topic, which is part of the regular mathematical curriculum everywhere in the world.
I publicly shared a formal article, while continuing to investigate mathematical history around quadratic equations. I found that the individual steps of this method had been separately discovered by ancient mathematicians, and some deep digging unearthed modern teachers who were on the same track. In retrospect, the combination of these steps is something that anyone could have come up with, which makes it more surprising that this method is not commonly known. However, I have not seen any previously-existing book or paper which states the same pedagogical method and justifies all steps consistently, and so I chose to share it to provide a safely referenceable version.