What is the quadratic formula and how is it derived?
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