Question

Solve using any method. $$ (9 x-2)(x+4)=28 x-9 $$

   Solve using any method.
$$
(9 x-2)(x+4)=28 x-9
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 9, Problem 62

Instant Answer

Solved by Expert Victor Salazar

02/05/2022

Step 1

Step 1: First, we expand the left side of the equation: $$ (9x - 2)(x + 4) = 9x^2 + 36x - 2x - 8 = 9x^2 + 34x - 8 $$ Show more…

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Solve using any method. $$ (9 x-2)(x+4)=28 x-9 $$

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Key Concepts

Combining Like Terms

After expanding the binomials, similar degree terms in the polynomial are added together to simplify the expression. This process reduces the complexity of the equation and is a fundamental step in solving algebraic equations.

Rearranging Equations

Rearranging equations involves moving all terms to one side of the equation to set it equal to zero. This standard form is essential for applying methods such as factoring or using the quadratic formula to find the solutions of the equation.

Expansion of Binomials

This concept involves applying the distributive property, often referred to as the FOIL (First, Outer, Inner, Last) method, to multiply two binomials. It allows the expression of the product in an expanded polynomial form, which is essential for simplifying and solving the equation.

Factoring Quadratic Equations

Factoring is a method used to express a quadratic equation as a product of simpler expressions, typically binomials. Recognizing patterns such as perfect square trinomials or applying techniques like splitting the middle term can simplify the process of finding the equation’s roots.

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