Two surprising things I found that improved my imaging and staging...

One of the biggest mistakes, IMHO, made with spkr placement is many people instinctually place them way too far apart.  Thinking it will present a large stage, image etc..  This will usually have the opposite effect and will damage the overall SQ. 

It "may" seem like its large, but once moved to proper center to center distance (as well as the other dimensions), things lock in and SQ is improved significantly many times.  The 1/3 rule and cardas calculation are good starting points / ballpark and reveals how far off people miss the space between, distance from side and rear walls. 

Understanding shared spaces present a lot of restrictions on placement, so it's always a compromise and there are no exact formulas for placement, just guidelines - but those guidelines (physics) usually provide pretty consistent results.

However, if you have the ability to at least try some of these "guidelines" its worth it, for no other reason than getting experience.  Even better, when the wife is gone, remove some of the furniture "in the way" temporarily, move the spkrs out into the room as well as play with the listening position, just to hear what your system can or should sound like.  Understanding your room acoustically is massively important.  It does take work though. 

It really comes down to how much effort one wants to put in getting the most out of your rig and good enough is totally fine if that's what suits you.

Cardas method based on OPs link seems to address tempering bass response in the room....only.  Based on multiple reads, some people feel once you take care of bass all else falls into place.
I agree with previous poster, following cardas puts my speakers so darn deep into the room, can’t have it.
another method is to start with speakers against rear wall and inch them out until Bass calms down.
add owners manuals instructions for placement and it explains why I get nuts and move speakers so many times.
my personal favorite is to start with both speakers smug against rear wall, 2-3 ft in from side walls. Bring one speaker out until you only hear vocals coming from that speaker. Then bring out the other speaker until the vocals are centered again. Finally toe in until vocals are not more than 2ft wide. **2people needed for this method.
finally, you can call John Ruttan to come over to help you out with his ears and measuring instruments . I’ve seriously considered this but fear I may come away from the experience with an upgraded part I didn’t know I needed (but may very well love having).

One more point reg cardas method, placement is based on center point of woofer. My woofers are not in the center of the  speaker and are not mirror image.  So in my case one speaker is 20” from side wall, other speaker is 26”.
That may be right for bass but how can it be right for rest of spectrum?

Regarding rear wall and stuff between the speakers. I find it highly dependent on the speakers. My ribbon speakers didn’t seem to care that much about low racks (2.5’)  in between and liked the bare painted sheet rock behind them. My Sonus Faber Amati Traditional sound much better without the rack in between and with a thick Afghan rug covering the entire wall behind the speakers. 

Also, while the rule of thumb with my speakers is to toe them in to converge ~18” behind the listener… they sound much better in my room with no toe-in what so ever.

So, for me, it depends.

"It depends" is the fundamental law in small room acoustic for me...Because we must change a room with our ears and for them when listening a SPECIFIC speaker in the room...The frequencies response of the room in the vocal timbre bandwidth is the pilot guide to do this...You "bent" the room to what is better for your ears listening human voice with an active mechanical modification of the pressure zones distribution grid in the room not only with panels reflective, absorbing and diffusive in a passive treatment......

Why human voice?

Because the inner relation we have with all acoustical cues linked to the timbre of a human voice and his MEANING for us...All of us we can identify a correct timbre FOR EACH ONE OF US but which will not be "exactly" the same for none others save us...Then our small room must be fine tuned for our own ears/speakers specifically for a better human voice and instrument recognition when playing a note...

A great musical hall is not a small room....Acoustic laws cannot be used in the same way in this 2 cases....For example the use of reverberation time and the timing of the different first wavefronts cannot be the same in a great Hall and in my 13 feet square room...

No recipe works well for all small room because of their different geometry, topology and acoustical varied content...

No recipe will never compete or replace fine tuning of the small room...

But at the end this fine tuning of passive acoustic treatment and active mechanical control of any small room is the greater of all audio possible improvement with a specific pair of speakers...Greater than most upgrades of gear ....

Small room acoustic must be designed for specific speakers in specific small room...

A "tweak" like putting a rug can help, but we are short of a true fine tuning with some easy recipe of this nature only... Fine tuning is related to listening experiments and time but at possible low cost in my experience....

And any electronical equalization is a TOOL, not the solution at all...

For sure a dedicated audio room is the only essential  luxury in audiophile world...

I am not a scientist, but it is my experience with my room...