Solve for a variable inside a summation

[lilly92]

I need to solve the equation

for x, where a is a known constant and

.
The bs are known too.
What i need to do is sto find for which xs I'll have a specific value of a, eg a=0.5, i.e. solve for x and substitute the a. I believe that the result will be a group of xs and not a single x-value. Also the last two terms of the first equation are the expansion of the squared sum of the product xy

 

[mfb]

There are n variables "x", x₁ to x_n, but just one equation. Without additional assumptions or other information, there is no way to solve anything. You can fix all but one to an arbitrary value and then solve the equation for the last one (gives a simple quadratic equation), but I doubt that's what you actually want.

 

[Ray Vickson]

I need to solve the equation

for x, where a is a known constant and

.
The bs are known too.
What i need to do is sto find for which xs I'll have a specific value of a, eg a=0.5, i.e. solve for x and substitute the a. I believe that the result will be a group of xs and not a single x-value. Also the last two terms of the first equation are the expansion of the squared sum of the product xy

You have variables $x_1, x_2, \ldots, x_n$ but only one equation. Essentially, you have the equation of a quadratic surface in n-dimensional space. There will not be only a single solution, just as a surface does not contain only a single point.