Solving

Solving is the process of finding answers to questions or problems, transforming a question into a concrete outcome. It involves identifying unknowns, constraints, and relationships, and often verifying the result.

In mathematics, solving refers to determining the values of variables that satisfy a statement, such as solving equations, systems, or inequalities. Methods include algebraic manipulation, substitution, elimination, factoring, and, in higher mathematics, leveraging functions, matrices, calculus. Solutions may be exact or approximate, and existence and uniqueness are important considerations.

In computer science, solving a problem means producing an algorithm or procedure that correctly and efficiently yields a solution. This includes computational problem solving, designing algorithms, analyzing time and space complexity, and using automated solvers for constraints (SAT/SMT), optimization, or numerical computation. Some problems are undecidable in general.

In problem-solving practice, models such as Polya's four steps or heuristics guide approach: understand the problem, plan a solution, carry out the plan, and review/reflect. Creative and critical thinking, domain knowledge, and collaboration improve outcomes.

In everyday life and education, solving encompasses puzzles, practical decisions, and scientific inquiry. Verification and evaluation of solutions, alternatives, and potential side effects are important to ensure the result holds under different conditions.