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[PartlyCloudlike]

Hi, I was wondering if anyone can help me with this physics problem. It's an online problem and I've already completed parts b,c,d,e. But I can't get part A for the LIFE OF ME!!

You have 3 charges, 50, -20, and 70 nC, located at the vertices of an equilateral triangle of side 8 cm.
(a) If the only charges on the equilateral triangle are the 50 and -20 nC, what is the x-coordinate of the center of the circle that describes the equipotential of 0 volts?

OK, so first I set up V1+V2 = 0. Do some algebra and I have:
25/(x^2 + y^2) = 4 / ((8-x)^2 + y^2)
25y^2 + 25x^2 - 4x^2 - 400x -4y^2+ 1600 = 0
21x^2 + 21y^2 - 400x + 1600 = 0
x^2 + y^2 - 400x/21 + 1600/21 = 0

Now here's where I get stuck. I know I'm trying to get my numbers into the form (x - xo)^2+(y - yo)^2=r^2

But how do I get x0 and yo? And where do I go from here? I'd appreciate any help!

 

[GG-Duo]

you gotta do that whole thing where you
take this:

x^2 + bx + c

and turn it into this:

(x + p)^2 + q

 

[PartlyCloudlike]

I originallly had this, where x0 = 200/21. I used some very old notes to get through this portion but I'm not sure exactly if its the correct way to go about it.

x^2 - 400x/21 + (200/21)^2 - (200/21)^2 + y^2 + 1600/21 = 0
(x-200/21)^2 + (y-0)^2 = (200/21)^2 - 1600/21

 

[PartlyCloudlike]

OK I GOT THE ANSWER THANKS!