Talk:Completing the Square
While making this result as general as possible, placing it in the realm of commutative algebra with the language of "commutative and unitary ring" serves to make it inaccessible to students who are still at the level of elementary algebra.
We have had a raging battle on this topic in the past, in several contexts, but it's one we are doomed to repeat. My personal view is that there should be multiple (possibly nested) pages, from the general to the particular (or the particular to the general) where the "arithmetical" result is given first, and the result as it applies to commutative rings as a "general" version -- or, present the most general first, and then add the "particularisation" where the fact that the real numbers form a commutative ring with unity is used as one of the proofs.
In that way, the high-school student just learning algebra, or the early-undergraduate hacking through complicated integrations, will not be confused and sidetracked by a topic which is usually encountered considerably later in a degree course. --prime mover (talk) 15:12, 28 July 2017 (EDT)
- Yes, keeping the site accessible is a reasonable objective. I'd say first the common result, then the generalization. So, in this case, we add just Let $a,b,c,x$ be real numbers? I don't like when there's no context at all. --barto (talk) 18:25, 28 July 2017 (EDT)
- Sounds reasonable. Other instances of where we had this sort of thing: defining the Cauchy criterion in the context of real analysis and the wider context of metric spaces and then (IIRC) more general Hausdorff spaces. More challenging an exercise to keep everyone happy. --prime mover (talk) 18:30, 28 July 2017 (EDT)