Associated Topics || Dr. Math Home || Search Dr. Math

### Completing the Square Using a Diagram

```
Date: 11/09/1999 at 00:08:15
From: Andy Ko
Subject: Completing the square with diagram

My question involves completing the square, but instead of the usual
form of brackets and formula, I have to do it something like this:

x^2 + 6x + ...

+----------+-----+
|          |     |
|          |     |
|   x^2    | 3x  |
|          |     |
|          |     |
+----------+------
|          |
|    3x    |
+----------+

I don't know how to draw a diagram for completing the square for:

x^2 - 6x + ...

The answer is x^2 - 6x + 9, but I can't draw the diagram. My teacher
told me the only hint we get is that it overlaps. I can't seem to
figure it out. Can you help?

Thanks.
```

```
Date: 11/09/1999 at 11:00:45
From: Doctor Rob
Subject: Re: Completing the square with diagram

Thanks for writing to Ask Dr. Math.

Try this diagram:

x
o------------------o-----o
|        x-3       |  3  |
|                  |     |
|                  |     |
|x-3               |     |
|                  |     |
|                  |     | x
|                  |     |
|                  |     |
o------------------o-----o
|                  |     |
|3                 |     |
o------------------o-----o
x

The lower right has area 3^2. The entire lower edge rectangle (small
rectangle and square together making a longer rectangle) has area 3*x,
and likewise the entire right edge rectangle has area 3*x. They
overlap in the 3-by-3 square in the lower right corner.

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search