A-Level Mathematics: Completing The Square

Tuesday, 29 November 2011

C1 - Quadratic Equations - Completing the Square

Final method of solving quadratic equations is Completing the Square. By completing the square for :
$a x 2 + b x + c, you will generate the Quadratic Formula by solving for x.$

The general method consists of changing the quadratic in the form

$a x 2 + b x + c into (x+d)$ $2$ $+ e =0$

$where d = b/2 and e = b$ $2$ $/ 4$
$* This method requires a = 1, so if the coefficient of x is not 1 . Divide by a to get it to be 1.$

* Then rewrite the Formula in the form shown above. Solve for x by :

1) Taking e to the otherside and squarerooting it, and then subtracting b.

My image notes show two examples. 1) How to derive the quadratic formula 2) A numerical example :

Completing the Square Notes