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

which equation can be used to solve for x, the increase in side length of the square in inches?
x^2 + 4x – 81 = 0
x^2 + 4x – 65 = 0
x^2 + 8x – 65 = 0
x^2 + 8x – 81 = 0

Each side of the square needs to be enlarged by x inches to obtain the new area which is 81. The area of the square is calculated by squaring the measure of its side. 
                                         A = (x + 4)²
From the given value of area,
                                          (x +  4)² = 81
                                     x ² + 8x + 16 = 81
          
Further simplification leads to the answer,
                                         x² + 8x - 65 = 0