Where does the quadratic formula come from?

This is one of the most common a level math question. One which is essential to understand as it gives a firm understanding of core fundamental principles in math which are Completing the square and Algebra Manipulation.It is simple, you start with the general quadratic equation: ax^2 +bx + c = 0, and use the 'Complete the square' technique to this, and the with some algebra manipulation, you can reach the final quadratic formula.