Question

Solve the equation. $$ (x-7)(x+2)=x^{2}+4 x+13 $$

   Solve the equation.
$$
(x-7)(x+2)=x^{2}+4 x+13
$$

College Algebra Essentials

College Algebra Essentials

Julie Miller 1st Edition

Chapter 1, Problem 95

Instant Answer

Solved by Expert Erika Bustos

08/07/2021

Step 1

Step 1: First, we expand the left-hand side of the equation using the distributive property (also known as FOIL): \[ (x-7)(x+2) = x^{2}+2x-7x-14 = x^{2}-5x-14 \] Show more…

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Solve the equation. $$ (x-7)(x+2)=x^{2}+4 x+13 $$

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Key Concepts

Solving Linear Equations

In many cases, after simplification, an equation may reduce to a linear form. Solving a linear equation involves isolating the variable using basic algebraic manipulations, such as addition, subtraction, multiplication, or division.

Expanding Binomials

This concept involves using the distributive property (also known as the FOIL method for binomials) to multiply two binomials together. It is fundamental for transforming products into polynomial expressions, which are easier to work with in solving equations.

Simplification of Equations

After expanding expressions, combining like terms on both sides of an equation simplifies the equation and often eliminates common terms. This process reduces complexity and makes it possible to isolate the variable of interest.

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