Mathematical solutions refer to the methods and processes used to solve problems or equations in mathematics. These solutions can involve various techniques, such as algebraic manipulation, geometric reasoning, or numerical analysis. The goal is to find the value of unknown variables or to demonstrate a relationship between different mathematical entities. In many cases, mathematical solutions are represented as equations or formulas. For example, the Pythagorean theorem provides a solution for finding the length of a side in a right triangle. Understanding these solutions is essential for fields like engineering, physics, and economics, where mathematical principles are applied to real-world situations.