# What is the quadratic formula and how is it derived?

##### 1 Answer

Oct 25, 2015

For any general quadratic equation of the form

To derive this formula, we use completing the square in the general equation

Dividing throughout by a we get :

Now take the coefficient of x, half it, square it, and add it to both sides and rearrange to get

Now right the left hand side as a perfect square and simplify the right hand side.

Now taking the square root on both sides yields :

Finally solving for x gives