Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
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Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by several methods including factoring, graphing, using the square roots or the quadratic formula. Completing the square will always work when solving quadratic equations and is a good tool to have. Solving a quadratic equation by completing the square is used in a lot of word problems.I want you to follow the related link that explains the concept of completing the square clearly and gives some examples. that video is from brightstorm.
in division
The foil method in algebra is used to "multiply linear binomials."The FOIL method is used in elementary algebra as a guide for solving algebraic problems.
The graphical method is a method used to solve algebraical problems by using graphs.
When applying distributive property to solve an equation, you multiply each term by term. For instance: a(b + c) = ab + ac