The probability density function of the exponential distribution is defined as
$$ f(x;\lambda)=\begin{cases} \lambda e^{-\lambda x} &\text{if } x \geq 0 \\ 0 & \text{if } x<0 \end{cases} $$
We know that mle of the parameter $\lambda$ is $$\lambda = \frac{n}{\sum\limits_{i=1}^n x_i}$$ According to this solution, it seems $x \geq 0$ has no effect in the solution. My question is that why don't we use the constaint $x \geq 0$ in here? What happens when any of $x_i$'s less than zero?