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equation solving

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Also known as isolation of the unknown quantity, variable isolation

finding values for variables that make an equation true

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Encyclopedic overview

An example of using Newton–Raphson method to solve numerically the equation f(x) = 0

In mathematics, to solve an equation is to find the solutions of an equation, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality. A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set.

Excerpted from Wikipedia’s “equation solving” article, available under the CC BY-SA 4.0 licence.