> Normally, when we do a factoring problem, we are trying to find two numbers that multiply to 12 and add to 8. Those two numbers are the solution to the quadratic, but it takes students a lot of time to solve for them, as they’re often using a guess-and-check approach.

Wait... don't students apply the closed-form formula? Do we teach them that maths is about guessing? Next what? that pi is a rational number equal to 22/7, maybe?

https://www.poshenloh.com/quadratic/

It's a nice trick for equations with small nice numbers, that are common in math tests. But it fails spectacularly when you try to apply it to physics or chemistry problems that have decimals and nasty irrational solutions.

I don't like it, because it use that mathematicians like to put only nice numbers, even in topics like linear algebra or calculus that are about the real numbers.

But I don't mind something like this method for advanced math courses like Galois Theory, where the polynomials have integer or rational coefficients, and you can use the Gauss method https://en.wikipedia.org/wiki/Rational_root_theorem to find all the rational roots, that is quite similar to this "new" method.