Explain how theoretical and applied research complement each other.

Research methodology encompasses the systematic and structured process to conduct research and forms the backbone of any comprehensive study. It lays out the steps to be followed and the tools to be employed in gathering and analyzing data, as well as justifying the selected approach for a given research question.

Within research methodology, distinguishment is made between qualitative and quantitative approaches. Qualitative research delves into understanding concepts, thoughts or experiences and is often exploratory in nature. Alternatively, quantitative research deals with quantifiable data, utilizing statistical means to deduce patterns and relationships.

For instance, if the exercise is aimed at understanding the motivations behind student engagement, a qualitative approach might involve interviews to capture in-depth feelings and perspectives. On the other hand, a quantitative approach may use a survey to generate numerical data illustrating the frequency of certain behaviors.

Importantly, a robust research methodology ensures that theoretical constructs can be tested through applied research, thus strengthening the interconnectedness of theory and practical application.

The practical application of research refers to the use of research findings to solve real-world problems or enhance given aspects of life. It's in this realm that applied research becomes most visible, taking theories and conceptual framings and transforming them into actionable outcomes.

For example, research on learning styles may begin at the theoretical level to understand how individuals process information. However, this knowledge becomes applied as educators develop and implement diverse teaching strategies to accommodate different learning styles—the practical application of the research.

In health sciences, a new theoretical understanding of a disease mechanism might lead to applied research focused on developing a novel treatment or intervention. Such transitions from theory to practice are critical in fields such as medicine, engineering, and environmental sciences, where the emphasis is on creating tangible benefits and improvements.

Scientific theories are properly-substantiated explanations for natural phenomena. They are formulated through rigorous methods of observation, experimentation, and analysis, providing a comprehensive framework that can explain a wide range of facts or events. In essence, scientific theories are the endpoints of theoretical research—the 'why' behind the 'what'.

Take Newton's Law of Universal Gravitation as a classic example. It wasn't just a set of observations about falling apples; it was a theory that described the gravitational attraction between all masses. Similarly, the Theory of Evolution offers an explanation for the diversity of life through descent with modification over time.

Crucially, scientific theories are open to testing and falsification. The ability to be disproven is what distinguishes a theory from an untestable hypothesis or belief. A scientific theory's strength lies in its resilience to new findings, adjusting to incorporate more data or being replaced if a better theory emerges — reflecting the dynamic, evolving nature of scientific understanding.