Two charges located along x. Find all values?

[nawand]

Homework Statement

The first one has charge Q is at "-a" from origin the second is at "+3a" which is an unknown charge.What are the values for unknown charge if at the origin the net electric field they produce with magnitude 2Ke(Q/a²)

Homework Equations

Ke (Q/a²)i - Ke(q/9a²)=2Ke(Q/a²)i
if charge is negative
or
if the charge is positive
Ke (Q/a²)i - Ke(q/9a²)=-2Ke(Q/a²)i

The Attempt at a Solution

The question is how to choose signs for equation.
Attempt:
Assuming charge one is pointed towards the origin along x-axis so the sign will be "+i" and the second charge is pointed towards the origin in the negative x direction so tthe sign will be "-i".
Two possible values are at the origin: "+" or "-" 2Ke(Q/a²) .
If you choose "+" at the origin the answer will be -9Q. And for case chosen "-" sign in the origin, the answer will be 27Q so the particle has positive charge.
I wondering if this is the explanation?

 

[mfb]

Correct.

 

[nawand]

Thanks