I will assume that this room is rectangular. If so, its area is determined by
l • w = A
The length is (x + 7), and the width is (x + 3). We also know the area is 396 square feet. We can plug in and solve:
(x + 7) • (x + 3) = 396
x^2 + 3x + 7x + 21 = 396
x^2 + 10x + 21 = 396
x^2 + 10x - 375 = 0
x = 15
