Nonlinear multiariable equations

[Transstars]

I am working on a physics project whose subject is static electricity. There are several charges which create electrostatic forces and I want these forces to equal a certain value. I wrote the equations for these force but I couldn't figure out how to solve them. I would be pleased if someone could help me. Here are the equations:
A. q2/3.2875² - q3/0.0675² - q4/0.136² - q5/0.218² - q6/0.313 ² - q7/0.413²- q8/0.515²- q9/0.667²- q10/0.867²- q11/1.0475²- q12/1.212²- q13/1.2405²- q14/1.2765 ²= 44,63271604440628/kq1

B. q2/3.3005²+ q1/0.0675²- q4/0.0685²- q5/0.1505²- q6/0.2455 ²- q7/0.3455²- q8/0.4475²- q9/0.5995²-q10/0.7995² -q11/0.98²- q12/1.1445² -q13/1.2535² -q14/1.2895²=39,05362653885549/kq3

C. q2/3.232²+ q1/0.0136²+ q3/0.0685²-q5/0.082²-q6/0.177²- q7/0.277²-q8/0.379²- q9/0.531²-q10/0.731²- q11/0.9115²-q12/1.076²- q13/1.185²-q14/1.221²=45,87251371230645/kq4

D. q2/3.15²+ q1/0.218²+ q3/0.1505² +q4/0.082²- q6/0.095 ²- q7/0.195²-q8/0.297²- q9/0.449²- q10/0.649²- q11/0.8295²- q12/0.994²- q13/1.103²-q14/1.139²=55,79089505550785/kq5

E. q2/3.055² +q1/0.313 ²+q3/0.2455 ² +q4/0.177²+ q5/0.095 ²- q7/0.1²-q8/0.202²- q9/0.354²- q10/0.554²- q11/0.7345²- q12/0.899²- q13/1.005²-q14/1.044²=61,98988339500872/kq6

F. q2/2.955² +q1/0.413² +q3/0.3455²+ q4/0.277²+ q5/0.195²+ q6/0.1²- q8/0.102²- q9/0.254²- q10/0.454²- q11/0.6345²- q12/0.799²- q13/0.905²-q14/0.944²=61,98988339500872/kq7

G. q2/2.853² +q1/0.515²+ q3/0.4475²+ q4/0.379²+ q5/0.297²+ q6/0.202²+ q7/0.102²-q9/0.152²- q10/0.352²- q11/0.5325²- q12/0.697²- q13/0.803²-q14/0.842²=70,31762996319805/kq8

H. q2/2.7010² +q1/0.667²+ q3/0.5995²+ q4/0.531²+ q5/0.449²+ q6/0.354²+ q7/0.254²+ q8/0.152²- q10/0.2²- q11/0.3805²- q12/0.545²- q13/0.651²-q14/0.69²=32,8283821358275/kq9

I. q2/2.5010²+q1/0.867²+ q3/0.7995² + q4/0.731²+ q5/0.649²+ q6/0.554²+ q7/0.454²+ q8/0.352²+ q9/0.2²-q11/0.1805²- q12/0.345²- q13/0.451²-q14/0.49²=32,8283821358275/kq10

J. q2/2.3205²+q1/1.0475²+q3/0.98²+q4/0.9115²+q5/0.8295²+q6/0.7345²+q7/0.6345²+q8/0.5325²+q9/0.3805²+q10/0.1805²-q12/0.1645²-q13/0.2705²-q14/0.3095²=26,42684761934114/kq11

K. q2/2.156² +q1/1.212²+ q3/1.1445²+ q4/1.076²+q5 /0.994²+ q6/0.899²+ q7/0.799²+ q8/0.697²+ q9/0.545²+ q10/0.345²+q11 /0.1645²- q13/0.106²-q14/0.145²=27,5758409940951/kq12

L. q2/2.05² +q1/1.2405²+ q3/1.2535² + q4/1.185²+ q5/1.103²+ q6/1.005²+ q7/0.905²+ q8/0.803²+ q9/0.651²+ q10/0.451²+ q11/0.2705²+ q12/0.106²-q14/0.039²=6,65127868023947/kq13

M. q2/2.011² +q1/1.2765 ²+ q3/1.2895²+ q4/1.221²+ q5/1.139²+ q6/1.044²+ q7/0.944²+ q8/0.842²+ q9/0.69²+ q10/0.49²+ q11/0.3095²+ q12/0.145²+ q13/0.039²=2,926562619305367/kq14

k is a constant so it is not a variable.k=8.98*10^9
I know there are 14 variables whereas 13 equations. You can give q2 any value,if that helps you, however numerical value of all these variables including q2 must be above zero.
Variables:q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13,q14
You don't have to solve the equations for me(which would be great) but I would be very grateful if you can show me the wayto solve these equations.
If there is no way to solve these, please tell me.
Thanks
P.S:I'm sorry I didn't point it out. All expressions are in parentheses. I mean the equations go like that: (q2/3.2875²)- (q3/0.0675²⁾ - (q4/0.136²)-... The expressions are not the denominator of other expressions.

 

[Transstars]

q2/3.2875² - q3/0.0675² - q4/0.136² - q5/0.218² - q6/0.313 ² - q7/0.413²
- q8/0.515²- q9/0.667²- q10/0.867²- q11/1.0475²- q12/1.212²- q13/1.2405²
- q14/1.2765 ²= 718.38810708 / (k*q1)

Since k is common to all terms, plus a "q" also common (q1 in equation A), I suggest
you rewrite your equations, as I'm showing above for equation A.
At least, some navigation (without going nuts!) will be possible.

q2 being a given, then you basically have 13 equations, 13 unknowns.
Are you seriously considering solving for each unknown?
You do realise that, say using "elimination", you'll need to combine 2 equations
12 times before elimination one unknown, then 2 equations 11 times.... and so
on until you're down to 2 equations 1 time.
And you're not finished! Above starts over with 12 equations, 12 unknowns...
and so on...
By the way, the bracketing you mention is not required.

But there is a possibility that our local Sir Jonah, who excels at these whoppers,
steps in and puts us all to shame with a devious short cut...

Thank you for your comment
I do realize the complexity and silliness of these equations. I was hoping that there would be a method with matrices to solve these. If there is not such a thing to solve these then please excuse my unawareness of advanced methods since I am not an expert in advanced maths. By the way, I will rearrange the expressions-Thanks for the suggestion-

 

[Ishuda]

...I was hoping that there would be a method with matrices to solve these. ...

I don't know a formal solution but there is a matrix formulation. One computational solution would involve pseudo inverses of matrices, see
http://en.wikipedia.org/wiki/Generalized_inverse
and a simple 'guessing algorythm' to reduce an error function to zero. If you assigned q2 a value the matrices would be square otherwise there would be 14 row and 13 columns (or the other way around for a different, but equivalent, formulation)

The paper at
http://arxiv.org/ftp/arxiv/papers/0804/0804.4809.pdf
discusses a computational algorythm for the pseudo inverse and present the Matlab code for an implementation..