In a recent article "A Simple Proof of the Quadratic Formula", professor Po-Shen Loh, provides a new proof of the quadratic formula, which also produces an easier and natural method for solving general quadratic equations that has the potential to demystify quadratic equations for students worldwide.
It's surprising how such an easier method remained almost entirely hidden for thousands of years, but if Loh's instincts are right, maths textbooks could be on the verge of a historic rewriting - and we don't take textbook-changing discoveries lightly.
Loh's method starts from the standard approach of trying to factor the quadratic x² + bx + c as (x − x1)(x − x2), where x1 and x2 are two numbers with sum −b and product c, but instead of focusing on the more commonly taught way to find two numbers that when multiplied make up c, usually by guessing, he uses an averaging technique that concentrates on the sum, providing a simple, but effective algorithm that solves the problem without the need to learn the quadratic formula.
In Loh's paper, he admits he would "be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic", but says the alternative technique – which combines steps pioneered by Babylonian, Greek, and French mathematicians – is "certainly not widely taught or known (the author could find no evidence of it in English sources)".
Find more details in the author page: https://www.poshenloh.com/quadraticdetail/