Car shakes at highspeed, wears inside of tires

Most common indicators are. Wheel alignment ( not enough Castor adjustment) worn tie rod end/s Incorrect size tyres ( you have to have the rim sizes the same on both sides ) even though you noticed a difference Loose steering box / rack or worn rack mount rubbers Probably the noise under the floor as the rack is bashed up and down from the wobble. What you describe is castor wobble and some makers recommend 0 castor when in fact the setting should be 1/2 to 1 1/2 degree positive.

Replace the shocks.

You didn't supply a lot of info but generally a consistent shake at a particular speed is caused by wheel balance being off. Before having the balance checked look at the wheels inside and outside. Many times you can get either mud or ice packed in that will disturb the balance.
If balance is good, then you need to have the front end components checked for wear. If the shaking is very violent, it may be what's known as "death wobble" which can stem from excessive wear of components, usually either ball joints or track bar but everything's suspect. If you have that you can't mistake it as the steering wheel feels like it is trying to rip right out of your hands!!!.

are your tires balanced? look for uneven tire wear to determine if you need an alignment or balancing

Might be a tire balance issue, or...
If your wheel alignment is out of specs, it can wear your tires and they will "feather" or "cup" and cause the tire to shake on the road.

If your car is a all wheel drive you might want to check your maintence on your differentials that might be it.

Most low speed wobbles are caused by a tire becoming out of round as it wears down the tread. Probably a front tire. Jack the tire just till it is off the ground and turn the tire looking at the clearance of the tire above the ground. Notice how much it changes as you go around. Try this with each tire to find the problem.

Tread separation will also cause this. The above procedure will also work for this.

Your tires are out of balance, or you have a bad tire. Take it to a local tire shop and have them re-ballanced and checked for improper wear or problems. Any bald tires, or tires with bubbles coming out of them should be replaced. If no damage or improper wear is noticed, just have them ballanced. Shouldnt cost much money at all.

My first inclination would be to have tires balanced, unless it started suddenly, or you feel or hear something different in steering.

the tires,check if theyre worn out,make sure you check the inside edgea,if they're wearing unevenly,replace them and get an alignment from someone you trust,make sure the caster/camber and toe are in spec.-toe and camber are tire wearing angles-camber the most-if the inside or outside edges are worn more,or when you drive and let go of the steering wheel,it tilts to one side,camber problem,make sure tires are inflated correctly,about 32-36 psi,check ur gas flap for bmw recommended pressures-u should be safe with what i gave you-so yeah,check tire pressures and wear-if tires feathered,too much toe in or out-this should take care of your problem,good luck