Kq1/(1+r) + Kq2/r = 0, making r =the distance away from q2 outside of the system to be the equilibrium point. so q1 is 1m + r distance away from the point, and q2 = r distance away from the point.

K's cancel out, you get:
q1/(1+r) + q2/r = 0
Some algebra, turns out r = -0.2m.

Does that mean the point is 0.2m inwards from q2->q1 instead of outside of the system?
aka: (q1) -----0.8m----(qe)--0.2--(q2), where qe = equilbirium point?

Also, arent there two points which are in equliibrium of the system? We did a problem in class similar to this and had 2 pointsat equlibrium. Any help is greatly appreciated.

Are you sure you're supposed to be using the first power of r in your equations ? How does the inverse square law pertain here ? When should you instead use the first power as you did here (hint : potential).

What is the definition of electric field strength ? What is the electric field strength at distance r from point charge q ? Show some equations to prove understanding.

This is correct. So you realise you were wrong to use the first power in your first attempt, correct ? Because there you were trying to find a zero potential point, which is NOT what the question was asking for.

So rewrite your first attempt using the second power of r and get a result and I'll check to see if it's right.

Yep [tex]r = R(1 + (\frac{q_2}{q_1})^{\frac{1}{2}})^{-1}[/tex] equates to 0.66666. That's what I got too using what I said above. I think it's doing the same thing.