# How To: Compare methods of solving quadratic equations

In this video the instructor shows the different methods of solving quadratic equations. There are many methods to solve quadratic equations each with its pros and cons, each method suitable for a particular situation. The first method to solve quadratic equation is factoring. The advantage of using this method is that it is quick and easy. But the problem is not all equations can be factored very easily. This method requires a lot of practice and intuition. Use this method when the discriminate is a perfect square which gives the factors as real numbers. Next is the square root method which is simple and fast. But it is common to forget the signs while using this method leading to errors. Use this method when the given equation can be written in the form of a square. This video compares different methods of solving quadratic equations.

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1. The Diagonal Sum method, a new method to quickly solve a quadratic equation that can be factored
2. The Double Number Line new method to solve a system of two inequalities
3. Using graphing calculators to solve ANY inequality and any system of inequalities
See book titled "New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)
References: Campusi.com; Bookfinder4you.com

From my experiences, I advise you to always proceed solving a quadratic equation in standard form ax^2 + bx + c = 0 in 2 steps. First step, find out if the equation can be factored? How? Solve it by the Diagonal Sum Method. It usually takes fewer than 3 trials. If it fails, then the equation is not factorable, and consequently, the quadratic formula must be used in the second step.

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