Some quadratic equations cannot be solved by factorising and so an alternative method is the quadratic formula. It is based on a method called completing the square.

Rule to remember:

  • \text{If a quadratic equation has the form}\hphantom{aaa}a{x^2} + bx + c = 0

    \text{Then it can be shown that} \hphantom{aaa} x=\dfrac{- b \pm \sqrt {{b^2} - 4ac}}{2a}

This tutorial shows you when to use it, clues that are given in a question and common mistakes that are often made.

How to Derive the Quadratic Formula