An important factor to the success of BWO is the balancing between exploration and exploitation. The capacity to explore and exploit is largely governed by the balancing factor (B_f) and the probability of whale fall (W_f). Unfortunately, BWO exhibits delayed convergence and easily falls into local optima, much like other population-based algorithms. This is due to an imbalance between exploration and exploitation. This work proposes a modified version of the beluga whale optimization (BWO) termed BWO-MWF in an effort to enhance BWO. A modified probability of whale fall is added in place of the original probability of whale fall that works to increase the probability of whale falling which helps to avoid falling into the local optimum. Computational tests are carried out utilizing four benchmark systems of nonlinear equations with varying dimensions and 26 benchmarking functions to assess the effectiveness of BWO-MWF. The statistical test of Wilcoxon and the non-parametric Friedman test are employed in this study. Empirical data indicates that BWO-MWF is more effective than other algorithms currently in use since it can solve most optimization problems and nonlinear equation systems with the best possible results.