### Home > AC > Chapter 12 > Lesson 12.4.2 > Problem 12-80

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. Homework Help ✎The number of tiles in Figure 211.

The number of the figure that contains 6558 tiles.

Substitute 211 into the equation for *x*.

Substitute 6558 into the equation for *y*.

6558 = (*x* − 1)(*x* + 2) + *x*

6558 = *x*² + *x* − 2 + *x*

6558 = *x*² + 2*x* + 2

Set the equation equal to zero.

0 = *x*² + 2*x* − 6556

Factor the expression.

0 = (*x* + 82)(*x* − 80)

*x* = −82 or 80

The figure number cannot be negative.

Figure 80