In the field of math, solving an equation means finding the values of functions and variables which satisfy the conditions of the equation. There is always at least one unknown and solving multiple unknowns requires the use of matrices. To solve an equation, it is frequently necessary to rearrange the variables, collect the terms and simplify the equation. Quite often, it is not so much the value of variable but the condition in terms of other variables which satisfy the equality. Once these conditions are found, the equation reaches the status of tautology, i.e. a statement which can be proven to be true.
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There are a range of possible objectives. Indeed the solution set (i.e. all possible solutions) consists of either one solution, all solutions, or any-one solution. Alternatively, the objective may be to find the solution which is the best in terms of satisfying some specified objective. Therefore the task of solving an equation implies that not all solutions are equal in this respect – for example some quadratic equations consist of a negative and positive number, in many real life situations the negative number is irrelevant such as consumption of a commodity. The above tool provides the solution to any solve equation questions and it is left to the user to determine the preferred solution. Applying one’s judgement in this respect is known as optimisation and not restricted to simply “solving an equation”.Problems of this nature are called optimization problems; solving an optimization problem is generally not referred to as “equation solving”.
