Least squares assuming functional form of the solution

I am trying to solve the following least squares problem:

$$b(\alpha)=A(\alpha,\beta)x(\beta)$$

However, the solution I get is really bad. That's why I am trying to use an alternative approach, which is to assume the functional form of $x(\beta)$ through the use of tunable parameters, say $x(\beta, a, c)$. How can I solve this problem in MATLAB for a least squares solution for those parameters?

[dpb]

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