I don't know how true it is but I've heard a few times that certain plants do a good job of removing VOCs from household air. You could try investigating this claim. Here's one page that mentions it.
http://www.thedailygreen.com/going-green/tips/best-plants-for-indoor-air-quality
My wife has trouble with a variety of VOCs. It might not be an option for you to store the carpet partially outstretched in your garage until most of the odour departs.
Carpets usually expand over time.
This is caused by the fabric, under felt and entire carpet construction to stretch, caused by people walking over it over extended periods of time.
It does not usually stretch as much as you show in your pictures. Possibly this happened because the material is sensitive to moisture and caused it to become more elastic. Moisture could be from spillage, leakage or frequent carpet washing.
Tools and techniques
If your carpet has been like that for a long time there could be irreversible damage. You could still see a crease or uneven surface after re stretching it.
Here is a nice tool (maybe you can rent one?) made specially for stretch repair.
But the more common tool is the kick stretcher and requires some elbow great!
How to do it?
- You will need to completely undo one side of the carpet. Pick the easiest side to undo.
- Make sure it is a side that is parallel with the crease!
- In you case it looks like either the side near the tiled floor or the opposite side.
- Then depends on the tool you will need to stretch the entire carper, from left to right on the length it needs to be stretched. Otherwise if you do it unevenly other creases will appear.
- If possible you should put a new or check if the existing carpet gripper little hooks are still OK! These really help keep the carpet in place.
- Keep on stretching and smoothing the carpet until you are satisfied, do this slowly and evenly.
Too much pressure from either tool could tear the carpet. So be careful. If in doubt, call a professional.
In case your carpet is loose
I just had another look at it looks like your carpet is more like a large rug? :)
In that case, where you do not have grippers on one side you could opt into buying some hard underlay.
Remove the entire carpet aka rug and glue the underlay to the carpet. I would not do it inside the home because it requires a special type of glue that really stinks and needs about 24 hours to bond properly, in a fairly warm and dry environment.
Thanks to the underlay, depending on what you choose your carpet will be warmer to the foot but also help keep it flat.
Best Answer
It is possible to replace a section of carpet if you have a piece that is large enough. To tell the truth you will be able to see the section in most cases, to see other splices look at the doorways that have carpet you can usually see a line, sometimes the “grain” of the carpet is wrong so it even shows worse.
If you have a large enough pice and want to try you can rent an seaming iron (or buy one for ~50$, seaming tape will also be needed, the place I used to rent my iron from usually had tape for .50 per foot.
Once you have your scrap, iron and tape a good sharp razor knife is needed cut your hole out. Place the scrap over the hole and rotate it 90 deg and see if one orientation looks better. Cut the scrap pice for a very tight fit. Cut 4 strips of the seaming tape longer than the sides,
Heat the iron make sure to have a place to set it as the hot glue will mess up the carpet between pieces. Make sure to do the most visible strip first and do the strip that will be least visible last. Place the first strip of tape under the first edge overlapping on the back side, place the hot iron on the tape it will take a second to heat the glue but you are also heating the back of the carpet. Start pulling the iron until it reached the end pressing the carpet into the glue. Pull iron out set on tray. Wait for that to cool. Once that is cool put another strip under and repeat, let cool, then repeat making sure to let each section cool before moving on until done.
As I said you may always see the spot but if you do a good job others may not notice it, don’t over vacuum this area it will look slightly different for a while but the beater bar on a vacuum can cause a runner, clip them if you see them at just slightly below the average height.
If you take this on let us know how it turns out. And good luck.