Completing the square

Completing the Square

Completing the square lets us take a quadratic in expanded form and put it in standard form.

Looking at the expanded form of a quadratic

ax2+bx+c

Let’s use the equation x2+6x+10 as an example

to complete the square take b and dived by 2

6÷2=3

then square the quotient of b divided by two

(3)2=9

Add this to the equation

ax2+bx++c

x2+6x+9+10

Now act as though you are factoring the quadratic but ignore c for now

(x+3)(x+3)

(x+3)2

Looking at the unfactored equation x2+6x+9+10 you have to account for the 9 added

To do this subtract 9 from 10 (subtract  from c)

10-9=1

This leaves you with

(x+3)2+1

Which is in the standard form

Here is a link to a video explaining how to complete the square

http://www.youtube.com/watch?v=xGOQYTo9AKY