What is Completing the Square? Definition and Examples


What is "completing the square"? Completing the square is the process of changing an expression like x2 + bx into a perfect square trinomial by adding (b/2)2 to x2 + bx.

For example, you can change x2 + 4x into a perfect square trinomial by adding (4/2)2 or 22 = 4 to x2 + 4x.

x2 + 4x + 4 = (x + 2)(x + 2) = (x + 2)2, so x2 + 4x + 4 is a perfect square trinomial.

Completing the square using algebra tiles

Algebra tiles

Using the algebra tiles above, complete the square for x2 + 4x.

First, use the algebra tiles to model x2 + 4x.

x squared plus four x

Completing the square with algebra tiles means that you will rearrange the tiles and add more tiles so that everything will look like a square. 

a. Rearrange the tiles above so that it begins to look like a square.

So far, you can see that it is beginning to look like a square. However, it is not a square just yet.

b. You can complete the square by adding 4 of the small green squares where you see the empty space.

Completing the square

Completing the square with a couple more examples 


1. For x2 + 6x + n, find the value of n that will complete the square.

n = (6/2)2

n = (3)2

n = 9

2. For x2 + -8x + n, find the value of n that will complete the square.

n = (-8/2)2

n = (-4)2

n = 16

Recent math words

  1. What is a Vector? Definition and Examples

    Feb 04, 22 05:28 AM

    What is a vector? Definition, explanations and easy to understand read life examples.

    Read More

  2. What are Vertical Angles? Definition and Examples

    Feb 03, 22 05:45 AM

    What are vertical angles? Definition, explanation and easy to understand examples.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: