How to Solve a Quadratic Equation by Factoring

Solving $3c^2 = 10c - 8$ by Factoring

Solving $2d^2 - 5d = 3$ by Factoring

Solving $169x^2 = 49$ by Factoring

Solving $25p^2 = 49$ by Factoring

Solving $36x^2 = 121$ by Factoring

A manufacturing technician is solving a factored quadratic equation, ${}(x - 20)(x - 55) = 0$, to determine the boundary values for a machine's pressure settings. Match each step of the standard three-step solution procedure with the correct action required to find and verify the values.

An inventory analyst at a distribution center is training a new hire on how to find the break-even points for a new product line. The break-even points are modeled by the factored quadratic equation $(x - 12)(x - 50) = 0$. Arrange the standard steps the analyst should teach the new hire to solve this equation in the correct order.

A retail manager is using a profit-analysis formula that has been simplified to the factored form ${}(p - 15)(p - 25) = 0$, where $p$ represents the price of an item in dollars. According to the standard three-step procedure for solving quadratic equations using the Zero Product Property, what is the first step the manager must take to find the price points that result in zero profit?

Solving Quadratic Equations: The Final Step

A project manager is calculating the time in weeks, $w$, when a project will reach a zero-cost balance using the equation $(w - 12)(w - 20) = 0$. To find the values for $w$, the first step in the standard solution procedure requires the manager to set each individual factor, $(w - 12)$ and $(w - 20)$, equal to the number ____.

A business planning assistant at a retail startup is using the standard three-step procedure to find break-even pricing levels modeled by a factored quadratic equation. According to this procedure, once the assistant has set each individual factor equal to zero (Step 1) and solved the resulting linear equations (Step 2), the entire process is complete and no further actions are necessary to verify the pricing solutions.

Standard Operating Procedure for Quadratic Analysis