A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What does the value of x in her solutions represent?

In (6 + x)(9 + x) = 88, x is added to both the original width of 6 ft and length of 9 ft, so it represents the amount each dimension changes. Solving gives x² + 15x − 34 = 0, or (x + 17)(x − 2) = 0, so the solutions are x = 2 and x = −17. These are two possible amounts by which the dimensions were changed, even though −17 would not give physically valid patio dimensions.

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