# Equation solving

1. Dec 28, 2011

### Mikca10

Hi,

I want to solve the following equation by x:

Ʃ(ai^x -b)^2 = C ,
where Ʃ is over all i, i = 1:N, and ^ means "to the power of"

How to find x from here?

Thanks!

2. Dec 28, 2011

### Staff: Mentor

Welcome to the PF.

What is the context of the question? Is it from schoolwork?

3. Dec 29, 2011

### alexfloo

Try expanding the quadratic that's in the sum. Then you should ultimately be able to turn it into one quadratic equation.

4. Dec 29, 2011

### AlephZero

It isn't a quadratic. The equation is $\sum(a_i^x -b)^2 = C$ , not $\sum(a_ix -b)^2 = C$

5. Dec 29, 2011

### alexfloo

Ah my mistake. Thanks a lot.

6. Dec 29, 2011

### Mikca10

it is not the homework, it's more like a part of a research problem.. my algebra class was long time ago.

7. Jan 4, 2012

### Mikca10

Anyone has a clue?

8. Jan 4, 2012

### alexfloo

If you want an analytical solution for the general case, I'd say (pretty confidently) that it just can't be done. If you have specific values for the a_i, then I'd try it numerically.