A 4-inch by 6-inch photograph is going to be enlarged through increasing each side by the similar amount. The new area is 168 square inches. How many inches is each dimension increased?
Let x = the amount each side is increased. Then, x + 4 = the new width and x + 6 = the new length. Because area is length times width, the formula using the latest area is (x + 4)(x + 6) = 168. Multiply using the distributive property on the left side of the equation: x^{2} + 6x + 4x + 24 = 168; combine such terms: x^{2} + 10x + 24 = 168. Subtract 168 from both sides: x^{2} + 10x + 24 - 168 = 168 - 168. Simplify: x^{2} + 10x - 144 = 0. Factor the trinomial: (x - 8)(x + 18) = 0. Set each factor equal to zero and solve: x - 8 = 0 or x + 18 = 0; x = 8 or x = -18. Reject the negative solution since you won't have a negative dimension. The correct solution is 8 inches.