Math Help - Proof of Quadratic Formula

This section of Math Help online shows you the proof of quadratic formula. The quadratic formula is very important and should be learned.

The proof of quadratic formula

If  ax ² + bx + c = 0

Then diving the above quadratic equation by a gives:

Re arranging the above quadratic equation gives:

Here comes the neat trick to solve this quadratic equation, add   b 2 / 4a 2 to both sides of the quadratic equation in order to complete square on the left hand side. This gives the resulting quadratic equation:

Then factorizing the left hand side of the quadratic equation gives:

Re-arranging the right hand side of the quadratic equation gives:

Then it is a matter of taking square root of the right hand side and rearranging the quadratic equation as shown below: