CPM Homework Help : AC Problem 12-80

If a tile pattern can be described by the equation $y = (x − 1)(x + 2) + x$ , where $x$ represents the figure number and $y$ represents the number of tiles, find each of the following.

The number of tiles in Figure 211.
The number of the figure that contains $6558$ tiles.

Hint (a):

Substitute $211$ into the equation for $x$ .

Hint (b):

Substitute $6558$ into the equation for $y$ .

Step (b):

$6558 = (x − 1)(x + 2) + x$

$6558 = x^² + x − 2 + x$

$6558 = x^² + 2x + 2$

Step (b):

Set the equation equal to zero.

$0 = x^² + 2x − 6556$

Step (b):

Factor the expression.

$0 = (x + 82)(x − 80)$

$x=−82$ or $80$

Step (b):

The figure number cannot be negative.

Answer (b):

Figure $80$