A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.

Let x be the number of inches added to each side. The new side length is 4 + x, so its area is (4 + x)². Setting that equal to 81 and expanding gives x² + 8x + 16 = 81, or x² + 8x − 65 = 0. This is choice C.

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