In a warehouse inventory system, storage bins are labeled with consecutive odd integers. A technician needs to identify two bins where the product of their labels is 255. Based on the standard problem-solving strategy, which quadratic equation in standard form correctly represents this relationship?

In an industrial coding system, items are tracked using pairs of consecutive odd integers. For a specific quality check, the product of these integers must be ${}255$. To verify the IDs, technicians use a multi-step algebraic process. Match each mathematical expression or set of values with its specific role in this problem-solving process.

In a secure logistics facility, two adjacent storage bays are assigned ID numbers that are consecutive odd integers. For auditing purposes, the product of these two ID numbers must be 255. Arrange the following algebraic steps in the correct order to solve for the two possible pairs of bay ID numbers.

In an automated manufacturing plant, sensors on a conveyor belt are assigned numeric IDs that are consecutive odd integers. If the product of two adjacent sensor IDs is ${}255$, then the pair $-17$ and $-15$ represents a valid set of sensor IDs.

Auditing Consecutive Integer Pairs

A software developer is writing a script to generate security keys based on pairs of consecutive odd integers. The script must find two keys whose product is 255. By setting up the equation $n(n + 2) = 255$ and factoring the standard form $n^2 + 2n - 255 = 0$, the script will identify two valid sets of integer pairs. The positive pair is 15 and 17, and the negative pair is -17 and ____.

Documenting Algebraic Steps for Inventory Codes