As a facilities coordinator, you are tasked with ordering a custom rectangular sign for the main lobby. The sign maker states the area will be 30 square feet, and the length will be exactly one foot longer than the width. You set the width as $w$ and the length as $w + 1$. After substituting these into the area formula and expanding, you get the equation ${}30 = w^2 + w$. To solve this using the factoring method, what is the next critical step you must recall to put the equation in standard form?

As an office manager, you are ordering a custom rectangular sign for the department lobby. The sign must have an area of ${}30$ square feet, and the length must be exactly one foot more than the width. Arrange the following steps in the correct order to solve for the sign's dimensions using the geometry problem-solving strategy.

As a facilities coordinator for your company, you are verifying the dimensions for a rectangular sign with an area of ${}30$ square feet. The sign's length is designed to be one foot more than its width ($w$). After solving the resulting quadratic equation $w^2 + w - 30 = 0$, you find two algebraic solutions: $w = 5$ and $w = -6$. True or False: Both $w = 5$ and $w = -6$ are valid measurements for the physical width of the sign.

As a facilities coordinator for your office building, you are placing an order for a custom rectangular sign. The sign is required to have an area of 30 square feet, and the length must be one foot more than the width ($w$). Match each component of the geometry problem-solving strategy with its correct algebraic representation.

Applying Algebra to Commercial Signage

Determining Real-World Sign Dimensions from Quadratic Solutions

As a corporate facilities coordinator, you are ordering a custom rectangular logo sign with an area of 30 square feet. The sign's length is designed to be one foot more than its width. Letting $w$ represent the width, the length is written as $w + 1$. When substituting these into the area formula, you get the equation ${}30 = (w + 1)w$. To solve for $w$ by factoring, you must first rewrite this equation in standard quadratic form, which is $w^2 + w - 30 =$ ____.