Completing the Square

This is an x. Show me x2.

x x2

Show me x2 + 6x

Completing the Square

x2

x2

x x xx x x

Completing the Square

The picture is now x2 + 6x + 9,

How many units are required to complete the square?

which factors (x+3)(x+3) = (x+3)2

9!

x2xxx

x x x

1

1

1

1 1

1

1

1

1

Let’s Try Another One!

Show me x2 + 2x

x2 x x

Completing the Square

x2

How many units are required to complete the square?

x2

The picture is now x2 + 2x + 1

which factors (x+1)(x+1) = (x+1)2

1!

Last One with Manipulatives

Show me x2 + 8x

x2 x xx x x x x x

Completing the Square

Again, how many units are required to complete the square?

16

So, the picture is now x2 + 8x + 16

which factors (x+4)(x+4) = (x+4)2

Hard One!

Complete the square for x2 + 18x + ___

How many units are needed?

There are not enough pieces to do this problem.

Can we do it using paper and pencil?