A quadratic equation ax^2 + bx + c = 0 can be solved in two ways. One is by factorization, this involves writing ax^2 + bx + c = 0 as (x - x1)(x - x2) = 0. The roots are x1 and x2.

If it is not possible to do this we can use the formula for the roots which is x1 = [-b + sqrt(b^2 - 4ac)]/2a and x2 = [-b - sqrt(b^2 - 4ac)]/2a

When the roots are whole numbers or simple fractions, the first method is easy to use. The second works for all quadratic equations though it is a little tedious.

There are many ways to solve quadratic equations. For example, you can solve them in the following ways:

- By factoring.
- By taking square roots
- By completing the square
- By using the quadratic formula

There are 5 existing methods to solve quadratic equations.

**1. The graphing method.** It can only give approx. answers while true answers are sometimes numbers and fractions. Graphing a parabola takes lot of time as compared to other methods.

**2. The method of completing the square**. It works when a = 1. When a is not 1 and when the constants a, b, and c are large numbers, guessing and arranging the perfect square consume too much time.

**3. The quadratic formula**. It works for any type of quadratic equations. It is simple and fast. However, if the constants are large numbers and if you can not use calculators, in some tests/exams for example, you may have hard calculating difficulties. In addition, calculators give answers in decimals while true answers are sometimes in fractions (2/3, 4/7...). You also have to learn by heart the formula, that is pretty hard to remember.

**4.** The factoring method. It only works when the given equation is factorable. There is on YOU TUBE an interesting approach for factoring quadratic equations called the "ac" method, that you need to see.

**5.** The new **diagonal sum method.** It is a trial and error method, same as the factoring one. It is considered as a **shotcut **of the factoring method. When a = 1, it is very fast and it doesn't need factoring. To know about it, please read the article titled:"How to solve quadratic equations by the diagonal sum method" on this Enotes website.

The standard equation of a quadratic is: ax^2 + bx + c = 0

The 3 most used methods of determining a quadratic are:

1)Factoring.

The quadratic can be written as a product of linear factors, when knowing its roots.

ax^2 + bx + c = a(x-x1)(x-x2) x1 and x2 are the roots of the equation

2)Completing the square.

3) The quadratic formula

x1 = [-b+sqrt (delta)]/2a

delta = b^2 - 4ac

x2 = [-b-sqrt (delta)]/2a