# What is Completing the Square? Definition and Examples

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

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

x^{2} + 4x + 4 = (x + 2)(x + 2) = (x + 2)^{2}, so x^{2} + 4x + 4 is a perfect square trinomial.

## Completing the square using algebra tiles

Using the algebra tiles above, complete the square for x^{2} + 4x.

First, use the algebra tiles to model x^{2} + 4x.

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 with a couple more examples

**1.** For x^{2} + 6x + n, find the value of n that will complete the square.

n = (6/2)^{2}

n = (3)^{2}

n = 9

**2.** For x^{2} + -8x + n, find the value of n that will complete the square.

n = (-8/2)^{2}

n = (-4)^{2}

n = 16

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