Chapter A.4, Problem 29E

BuyFind*arrow_forward*

7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

*In Exercises 25 to 32, solve each quadratic equation by factoring.*

To determine

**To solve:**

The quadratic equation by factorization.

Explanation

Solving an equation is to find the value of the unknown variables in the equation, such that the obtained value or values of the unknown should satisfy the equation from which it was derived. Such a value is said to be the solution for the equation. In general a quadratic equation has two solutions for the variable in the equation as the degree of the equation is two.

**Calculation:**

Given,

The above equation is not in the standard form of a quadratic equation.

Add,

Since; addition is associative,

Now, we shall proceed with the factorization of the quadratic expression in the left of the equation.

First look for the common factor

But, here the

Thus, factor the expression

First factorize the product of the coefficient of the first tern and the constant, such that the sum of the factors gives the coefficient of the middle term.

Thus, factorize

Now, split the middle term

Hence, the given equation becomes

Factor out the common factors form the first two terms and form the last two terms of the above expression

Sect-A.1 P-1ESect-A.1 P-2ESect-A.1 P-3ESect-A.1 P-4ESect-A.1 P-5ESect-A.1 P-6ESect-A.1 P-7ESect-A.1 P-8ESect-A.1 P-9ESect-A.1 P-10E

Sect-A.1 P-11ESect-A.1 P-12ESect-A.1 P-13ESect-A.1 P-14ESect-A.1 P-15ESect-A.1 P-16ESect-A.1 P-17ESect-A.1 P-18ESect-A.1 P-19ESect-A.1 P-20ESect-A.1 P-21ESect-A.1 P-22ESect-A.1 P-23ESect-A.1 P-24ESect-A.1 P-25ESect-A.1 P-26ESect-A.1 P-27ESect-A.1 P-28ESect-A.1 P-29ESect-A.1 P-30ESect-A.2 P-1ESect-A.2 P-2ESect-A.2 P-3ESect-A.2 P-4ESect-A.2 P-5ESect-A.2 P-6ESect-A.2 P-7ESect-A.2 P-8ESect-A.2 P-9ESect-A.2 P-10ESect-A.2 P-11ESect-A.2 P-12ESect-A.2 P-13ESect-A.2 P-14ESect-A.2 P-15ESect-A.2 P-16ESect-A.2 P-17ESect-A.2 P-18ESect-A.2 P-19ESect-A.2 P-20ESect-A.2 P-21ESect-A.2 P-22ESect-A.2 P-23ESect-A.2 P-24ESect-A.2 P-25ESect-A.2 P-26ESect-A.2 P-27ESect-A.2 P-28ESect-A.2 P-29ESect-A.2 P-30ESect-A.2 P-31ESect-A.2 P-32ESect-A.2 P-33ESect-A.2 P-34ESect-A.2 P-35ESect-A.2 P-36ESect-A.3 P-1ESect-A.3 P-2ESect-A.3 P-3ESect-A.3 P-4ESect-A.3 P-5ESect-A.3 P-6ESect-A.3 P-7ESect-A.3 P-8ESect-A.3 P-9ESect-A.3 P-10ESect-A.3 P-11ESect-A.3 P-12ESect-A.3 P-13ESect-A.3 P-14ESect-A.3 P-15ESect-A.3 P-16ESect-A.3 P-17ESect-A.3 P-18ESect-A.3 P-19ESect-A.3 P-20ESect-A.3 P-21ESect-A.3 P-22ESect-A.3 P-23ESect-A.3 P-24ESect-A.3 P-25ESect-A.3 P-26ESect-A.3 P-27ESect-A.3 P-28ESect-A.3 P-29ESect-A.3 P-30ESect-A.3 P-31ESect-A.3 P-32ESect-A.4 P-1ESect-A.4 P-2ESect-A.4 P-3ESect-A.4 P-4ESect-A.4 P-5ESect-A.4 P-6ESect-A.4 P-7ESect-A.4 P-8ESect-A.4 P-9ESect-A.4 P-10ESect-A.4 P-11ESect-A.4 P-12ESect-A.4 P-13ESect-A.4 P-14ESect-A.4 P-15ESect-A.4 P-16ESect-A.4 P-17ESect-A.4 P-18ESect-A.4 P-19ESect-A.4 P-20ESect-A.4 P-21ESect-A.4 P-22ESect-A.4 P-23ESect-A.4 P-24ESect-A.4 P-25ESect-A.4 P-26ESect-A.4 P-27ESect-A.4 P-28ESect-A.4 P-29ESect-A.4 P-30ESect-A.4 P-31ESect-A.4 P-32ESect-A.4 P-33ESect-A.4 P-34ESect-A.4 P-35ESect-A.4 P-36ESect-A.4 P-37ESect-A.4 P-38ESect-A.4 P-39ESect-A.4 P-40ESect-A.4 P-41ESect-A.5 P-1ESect-A.5 P-2ESect-A.5 P-3ESect-A.5 P-4ESect-A.5 P-5ESect-A.5 P-6ESect-A.5 P-7ESect-A.5 P-8ESect-A.5 P-9ESect-A.5 P-10ESect-A.5 P-11ESect-A.5 P-12ESect-A.5 P-13ESect-A.5 P-14ESect-A.5 P-15ESect-A.5 P-16ESect-A.5 P-17ESect-A.5 P-18ESect-A.5 P-19ESect-A.5 P-20ESect-A.5 P-21ESect-A.5 P-22ESect-A.5 P-23ESect-A.5 P-24ESect-A.5 P-25ESect-A.5 P-26ESect-A.5 P-27ESect-A.5 P-28ESect-A.5 P-29ESect-A.5 P-30ESect-A.5 P-31ESect-A.5 P-32ESect-A.5 P-33ESect-A.5 P-34ESect-A.5 P-35ESect-A.5 P-36ESect-A.5 P-37ESect-A.5 P-38ESect-A.5 P-39E

Single Variable Calculus

Mathematical Applications for the Management, Life, and Social Sciences

Calculus: Early Transcendental Functions

Essentials Of Statistics

Mathematical Excursions (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Intermediate Algebra

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus: Early Transcendentals

Calculus (MindTap Course List)

Finite Mathematics

Elementary Technical Mathematics

Multivariable Calculus

Understanding Basic Statistics

Calculus: An Applied Approach (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Calculus of a Single Variable

Elements Of Modern Algebra

Trigonometry (MindTap Course List)

Contemporary Mathematics for Business & Consumers

Single Variable Calculus: Early Transcendentals

Calculus: Early Transcendental Functions (MindTap Course List)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

Finite Mathematics for the Managerial, Life, and Social Sciences