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12-80.
  1. 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 ✎

    1. The number of tiles in Figure 211.

    2. 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 = x² + x − 2 + x

6558 = x² + 2x + 2

Set the equation equal to zero.

0 = x² + 2x − 6556

Factor the expression.

0 = (x + 82)(x − 80)

x = −82 or 80

The figure number cannot be negative.

Figure 80