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.
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.
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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