BuyFind

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
Publisher: Cengage,
ISBN: 9781337614085
BuyFind

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
Publisher: Cengage,
ISBN: 9781337614085

Solutions

Chapter
Section
Chapter A.4, Problem 38E
Textbook Problem

Determine the length x by solving either the equation x 4 = 6 x + 5 or the equivalent equation x x + 5 = 24 .

Chapter A.4, Problem 38E, Determine the length x by solving either the equation x4=6x+5 or the equivalent equation xx+5=24.

Expert Solution
To determine

To find:

The length ‘x’ by solving the equation xx+5=24.

Explanation of Solution

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,

xx+5=24

Apply the distributive property of multiplication over addition.

x·x+x·5=24

x2+5x=24

Add; -24 on both side,

x2+5x+-24=24+-24

x2+5x-24=0

The above equation is in the standard form of a quadratic equation.

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

First look for the common factor GCF of the terms x2, 5x and -24.

But, here the GCF is 1.

Thus, we have to factor the above equation by the reverse FOIL method.

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 -24 as -3·8 so that the sum of the factors (-3)+8 gives 5.

Now, split the middle term 5x as (-3x)+8x.

Hence, the equation becomes,

x2+-3x+8x-24=0

x·x+-3·x+8·x+8·-3=0

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

Want to see this answer and more?

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

See solution

Chapter A Solutions

Elementary Geometry For College Students, 7e
Show all chapter solutions
Ch. A.1 - Complete each division: a 12(3) c (12)(23) b...Ch. A.1 - Nine pegs are evenly spaced on a board so that the...Ch. A.1 - The four owners of a shop realize a loss of 240 in...Ch. A.1 - Bill works at a weekend convention by selling...Ch. A.1 - Use the Distributive Axiom to simplify each...Ch. A.1 - Use the Distributive Axiom to simplify each...Ch. A.1 - Simplify each expression: a 6+4 c 16x2y9x2y b...Ch. A.1 - Simplify each expression: a r2+2r2 c 7x2y+3xy2 b...Ch. A.1 - Simplify each expression: a 2+34 c 2+322 b (2+3)4...Ch. A.1 - Simplify each expression: a 32+42 c 32+(82)3 b...Ch. A.1 - Simplify each expression: a 8228 c 52637(2) b...Ch. A.1 - Use the FOIL method to complete each...Ch. A.1 - Use the FOIL method to complete each...Ch. A.1 - Use the FOIL method to complete each...Ch. A.1 - Using x and y, find an expression for the length...Ch. A.1 - The cardboard used in the construction of the box...Ch. A.1 - A large star is to be constructed, with lengths as...Ch. A.1 - The area of an enclosed plot of ground that a...Ch. A.1 - The degree measures of the angles of a triangle...Ch. A.1 - The right circular cylinder shown in the...Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - In Exercises 7 to 12, simplify by using the FOIL...Ch. A.2 - In Exercises 7 to 12, simplify by using the FOIL...Ch. A.2 - In Exercises 7 to 12, simplify by using the FOIL...Ch. A.2 - In Exercises 7 to 12, simplify by using the FOIL...Ch. A.2 - In Exercises 7 to 12, simplify by using the FOIL...Ch. A.2 - In Exercises 7 to 12, simplify by using the FOIL...Ch. A.2 - In Exercises 13 to 16, evaluate each expression....Ch. A.2 - In Exercises 13 to 16, evaluate each expression....Ch. A.2 - In Exercises 13 to 16, evaluate each expression....Ch. A.2 - In Exercises 13 to 16, evaluate each expression....Ch. A.2 - In Exercises 17 to 20, find the value of the...Ch. A.2 - In Exercises 17 to 20, find the value of the...Ch. A.2 - In Exercises 17 to 20, find the value of the...Ch. A.2 - In Exercises 17 to 20, find the value of the...Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation. 3x3=6Ch. A.2 - In Exercises 21 to 32, solve each equation. y3+2=6Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation. b=27b2Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation. x3x2=5Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 21 to 32, solve each equation....Ch. A.2 - In Exercises 33 to 36, find the value of the...Ch. A.2 - In Exercises 33 to 36, find the value of the...Ch. A.2 - In Exercises 33 to 36, find the value of the...Ch. A.2 - In Exercises 33 to 36, find the value of the...Ch. A.3 - If line segment AB and line segment CD in the...Ch. A.3 - Using the number line shown, write two...Ch. A.3 - If angles ABC and DEF in the accompanying drawing...Ch. A.3 - Consider the statement x6. Which of the following...Ch. A.3 - According to the definition of ab, there is a...Ch. A.3 - Does the Transitive Property of Inequality hold...Ch. A.3 - For Exercises 7 and 8, use the Trichotomy Property...Ch. A.3 - For Exercises 7 and 8, use the Trichotomy Property...Ch. A.3 - Of several line segments, ABCD the length of...Ch. A.3 - Of several angles, the degree measures are related...Ch. A.3 - Classify as true or false. a 54 c 45 b 55 d 55Ch. A.3 - Classify as true or false. a 54 c 55 b 54 d 55Ch. A.3 - Two angles are supplementary if the sum of their...Ch. A.3 - Two trim boards need to be used together to cover...Ch. A.3 - Consider the inequality 35. Write the statement...Ch. A.3 - Consider the inequality 69. Write the statement...Ch. A.3 - Suppose that you are solving an inequality....Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 18 to 28, first solve each...Ch. A.3 - In Exercises 29 to 32, the claims made are not...Ch. A.3 - In Exercises 29 to 32, the claims made are not...Ch. A.3 - In Exercises 29 to 32, the claims made are not...Ch. A.3 - In Exercises 29 to 32, the claims made are not...Ch. A.4 - Note: Exercises preceded by an asterisk are of a...Ch. A.4 - Note: Exercises preceded by an asterisk are of a...Ch. A.4 - Note: Exercises preceded by an asterisk are of a...Ch. A.4 - Note: Exercises preceded by an asterisk are of a...Ch. A.4 - In Exercises 5 to 8, factor each difference of two...Ch. A.4 - In Exercises 5 to 8, factor each difference of two...Ch. A.4 - In Exercises 5 to 8, factor each difference of two...Ch. A.4 - In Exercises 5 to 8, factor each difference of two...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - In Exercises 17 to 22, factor completely. 4x2-16Ch. A.4 - In Exercises 17 to 22, factor completely. 6y2-54Ch. A.4 - In Exercises 17 to 22, factor completely....Ch. A.4 - In Exercises 17 to 22, factor completely....Ch. A.4 - In Exercises 17 to 22, factor completely....Ch. A.4 - In Exercises 17 to 22, factor completely....Ch. A.4 - In Exercises 23 to 24, find the three factors for...Ch. A.4 - In Exercises 23 to 24, find the three factors for...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 33 to 36, solve each incomplete...Ch. A.4 - In Exercises 33 to 36, solve each incomplete...Ch. A.4 - In Exercises 33 to 36, solve each incomplete...Ch. A.4 - In Exercises 33 to 36, solve each incomplete...Ch. A.4 - Given that the area of the rectangle shown is 66,...Ch. A.4 - Determine the length x by solving either the...Ch. A.4 - Find the length a by solving the equation...Ch. A.4 - With the highest degree term being 4x3, the...Ch. A.4 - With the highest degree term being x4, the...Ch. A.5 - Use your calculator to find the approximate value...Ch. A.5 - Use your calculator to find the approximate value...Ch. A.5 - Which equations are quadratic? a 2x25x+3=0 d...Ch. A.5 - Which equations are incomplete quadratic...Ch. A.5 - Simplify each expression by using the Product...Ch. A.5 - Simplify each expression by using the Product...Ch. A.5 - Simplify each expression by using the Quotient...Ch. A.5 - Simplify each expression by using the Quotient...Ch. A.5 - Use your calculator to verify that the following...Ch. A.5 - Use your calculator to verify that the following...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 11 to 18, determine the values of a,...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 19 to 26, solve each equation by...Ch. A.5 - In Exercises 27 to 32, solve each incomplete...Ch. A.5 - In Exercises 27 to 32, solve each incomplete...Ch. A.5 - In Exercises 27 to 32, solve each incomplete...Ch. A.5 - In Exercises 27 to 32, solve each incomplete...Ch. A.5 - In Exercises 27 to 32, solve each incomplete...Ch. A.5 - In Exercises 27 to 32, solve each incomplete...Ch. A.5 - The length of a rectangle is 3 more than its...Ch. A.5 - To find the length of CP which is x, one must...Ch. A.5 - In Exercises 35 and 36, use Theorem 2.5.1 to solve...Ch. A.5 - In Exercises 35 and 36, use Theorem 2.5.1 to solve...Ch. A.5 - In Exercises 37-39, c2=a2+b2. In the right...Ch. A.5 - In Exercises 37-39, c2=a2+b2. In the right...Ch. A.5 - In Exercises 37-39, c2=a2+b2. In the right...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Show solutions
In problems 45-62, perform the indicated operations and simplify. 59.

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 1-6, simplify the expression. 11(1x)

Calculus: An Applied Approach (MindTap Course List)

In Exercises 16, find the points of intersection of the graphs of the functions. Express your answer accurate t...

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

Calculate y'. 45. y = ln( cosh 3x)

Single Variable Calculus: Early Transcendentals

In Exercises 710, find C(n,x)pxqnx for the given values of n, x and p. n=5,x=3,p=.2.

Finite Mathematics for the Managerial, Life, and Social Sciences

(f(x)g(x)) = f(x)g(x).

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

Classify the function as being even, odd, or neither.

College Algebra (MindTap Course List)

Present Value If you invest P dollars the present value of your investment in a fund that pays an interest rate...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Use Euler’s method to approximate y(1.2), where y(x) is the solution of the initial-value problem where x > 0....

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Grade Point Average Comparison. The grade point averages of 352 students who completed a college course in fina...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)