Question

Solve by factoring. $$11 x=2 x^{2}+12$$

   Solve by factoring.
$$11 x=2 x^{2}+12$$

Precalculus: Graphs and Models

Precalculus: Graphs and Models

Raymond A. Barnett,… 3rd Edition

Chapter 2, Problem 15

Instant Answer

Solved by Expert Ernest Castorena

06/20/2020

Step 1

We can do this by subtracting $11x$ from both sides of the equation: $$2x^{2} - 11x + 12 = 0$$ Show more…

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Solve by factoring. $$11 x=2 x^{2}+12$$

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Key Concepts

Rearrangement of Equations

In solving equations, especially quadratic equations, it is crucial to rearrange the equation so that all terms are on one side. This establishes a standard form where one side equals zero, which is necessary for applying techniques like factoring or using the quadratic formula.

Standard Form of Quadratic Equations

A quadratic equation is typically written in the standard form ax² + bx + c = 0. This format simplifies the process of identifying coefficients and applying various methods for solving the equation, such as factoring, completing the square, or using the quadratic formula.

Factoring Quadratic Expressions

Factoring involves rewriting the quadratic expression as a product of simpler binomials. This technique is useful for solving the equation because once factored, the equation can be set equal to zero, allowing for the application of the zero product property to find the solutions.

Zero Product Property

The zero product property states that if the product of two or more factors is zero, then at least one of the factors must be zero. This fundamental property is used to solve factored quadratic equations by setting each factor equal to zero and solving for the variable.

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