Solving Quadratic Equations: What is the Most Efficient Method?
Because there are several techniques for solving quadratic equations, a preliminary analysis is useful to determine the method that minimizes both the arithmetic and algebraic calculations. Often, there is one method that stands out as the most efficient method; at other times, it can be a matter of hairsplitting to decide between two methods that are roughly equal in effort. Here is the order we recommend to find the Most Efficient Method.
First, if there is an obvious pattern that suggests a particular method, like an obvious factoring or the square root method, use it. Otherwise, start by testing various ways to factor the expression. If that does not work, consider using "Completing the Square" if the numbers are not too onerous. Finally, if the numbers are not easy to work with, use the quadratic formula.
Of course, even experts can disagree about what is the Most Efficient Method to solve a given quadratic equation.

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