Minimizing sum involving exponentials: $\sum_{k=1}^n (\exp(-a_k x) - b_k)^2$

Question

Let $a_1,\ldots,a_n$ be real positive numbers (some may be zero, but then they are irrelevant for the optimization problem), and $b_1,\ldots,b_n$ are arbitrary real numbers. I want to find the minimizer for the following expression: $$x^*\in\arg\min_{x\in\mathbb{R}}(\exp(-a_kx) - b_k)^2.$$ To do so I take the derivative w.r.t. $x$ and set it to zero, which yields the following equation: $$-2\sum_{k=1}^n a_k\exp(-a_kx^*)(\exp(-a_kx^*)-b_k) = 0.$$ Is it feasible to find a closed form solution of this nonlinear equation, or should I rely on numerical root finding techniques instead?