What should I do about a crack in the concrete slab in my living room?
This is not going to be the answer you wanted to hear, but here goes.

Although I cannot see the cracks up close, it appears that the cracks were created by the floor flexing in a fairly straight line.  The cracks wander in a band about a foot wide with some parallel and joining cracks.

My first plan of attack would be to remove a rectangle of the damaged and weakened concrete apx one foot wide by the length of the crack, apx 10 feet. This can be done with a small hand held jackhammer. ($30 to $40/day at rental store). Slightly bevel the edges back from the surface to create an inverted "V", so it is slightly wider at the bottom than the top.  Once the edges are clean of dust and chips,  carefully fill the open void with a mixture of concrete mix equivalent to a 5000 pound mix.  You can use a ready mixed in a bag, just add water. Keep the mixture a bit to the stiff side, not too wet. Fill the entire void  be sure to push the mix tightly against the existing concrete. Wetting the existing concrete isn't a bad idea. Trowel smooth.  Done.

The reason I would not recommend a quick fill fix is that there may be lots of other cracks below the surface. If you don't get a good solid patch, water could wick up through cracks or the hidden damage could compress or further separate in future shakes. Although it seems like a big job, a 1 foot by 10 foot removal and repair is not as bad as it sounds. With the proper tools, you should be able to do the whole job in 4 to 6 hours.   Good Luck