There are so far 8 most common methods to solve quadratic equations in standard form ax^2 + bx + c = 0. They are:
1, Graphing method that give approx. answers and takes too much time.
2. The FOIL factoring method that only works fine when a, b, c are small numbers and when a = 1.
3.The method of completing the squares that only works fine when a, b, c are small numbers, and when b is a even number, and when a =1
4. The quadratic formula that can solve any quadratic equation. However solving by formula feels like boring and tedious. When the equation can be factored, other methods may be simpler and faster.
5. The Bluma Method (Google or Yahoo Search)
6. The Diagonal Sum Method that directly find the 2 real roots, in the form of 2 fractions, knowing the sum (-b/a) and the product (c/a). The most advantage of this method is that it can immediately obtain the 2 real roots, when a = 1, without having to factor into two binomials.
7. So far, the factoring AC Method has been the most popular one to solve quadratic equations that can be factored. However, this method can be greatly improved if we apply into its solving process the Rule of Sign of a quadratic equation. Please read the article:"Solving quadratic equations by the new improved factoring AC method" on Google Search.
8. The new Transforming Method that may be the simplest and fastest one to solve quadratic equations that can be factored. To know how does this method work, read the math article:"Solving quadratic equations by the new Transforming Method " on Google Search.