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.
Using the algebra tiles above, complete the square for x2 + 4x.
First, use the algebra tiles to model x2 + 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 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