# Solving implicit equations (variable in summation) without the Symbolic Toolbox

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Siddharth Parimal on 28 Aug 2017
Edited: Sailesh Sidhwani on 31 Aug 2017
Hi, I am trying to solve implicit equation in the following general form without the Symbolic Toolbox.
n and N are inputs, and the corresponding parameters (Ci, Ki and Cj, Qj) are known. But I need to automate this calculation for different values of n and N based on what I need.
I am struggling with writing the mathematical expression for a series without using a symbol for a variable. There are other solutions for solving implicit equations without Symbolic Toolbox, but I get stuck when I try to generalize them for a series.
Any help would be greatly appreciated.
Thanks, SP

Sailesh Sidhwani on 31 Aug 2017
Edited: Sailesh Sidhwani on 31 Aug 2017
Assuming C,K and Q are vectors. You can write your implicit equation as an anonymous function "fun" as follows:
fun = @(x) x + sum((C(1:n)+x) ./ (K(1:n)*x*x)) + sum((C(1:N)*x) ./ (Q(1:N)+x))
Now you can pass this anonymous function "fun" to "fsolve" to solve your implicit equation. You can find the "fsolve" documentation below: https://www.mathworks.com/help/optim/ug/fsolve.html
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Sailesh Sidhwani on 31 Aug 2017
Thanks Alan for pointing that out.