Samantha owns a rectangular field that has an area of 3,280 square feet. The length of the field is 2 more than twice the width. What is the width of the field?
Let w = the width of the ?eld and let 2w + 2 = the length of the ?eld (two more than double the width). Since area is length times width and multiply the two expressions together and set them equal to 3,280: w(2w + 2) = 3,280. Multiply by using the distributive property: 2w2 + 2w = 3,280. Subtract 3,280 from both sides: 2w2 + 2w - 3,280 = 3,280 - 3,280; simplify: 2w2 + 2w - 3,280 = 0. Factor the trinomial fully: 2(w2 + w - 1640) = 0; 2(w + 41)(w - 40) = 0. Set each factor equal to zero and solve: 2 ≠ 0 or w + 41 = 0 or w - 40 = 0; w = -41 or w = 40. Reject the negative solution since you will not have a negative width. The width is 40 feet.