Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Basic Mathematics Review » Exercise Supplement

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Elementary Algebra"

    Comments:

    "Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This module is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange GroveAs a part of collection: "Elementary Algebra"

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Elementary Algebra"

    Comments:

    "Elementary Algebra covers traditional topics studied in a modern elementary algebra course. Written by Denny Burzynski and Wade Ellis, it is intended for both first-time students and those […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: This module is from Elementary Algebra</link> by Denny Burzynski and Wade Ellis, Jr. Methods of solving quadratic equations as well as the logic underlying each method are discussed. Factoring, extraction of roots, completing the square, and the quadratic formula are carefully developed. The zero-factor property of real numbers is reintroduced. The chapter also includes graphs of quadratic equations based on the standard parabola, y = x^2, and applied problems from the areas of manufacturing, population, physics, geometry, mathematics (numbers and volumes), and astronomy, which are solved using the five-step method. This module contains an exercise supplement for the chapter "Quadratic Equations".

Exercise Supplement

Solving Quadratic Equations ((Reference)) - Solving Quadratic Equations by Factoring ((Reference))

For the following problems, solve the equations.

Exercise 1

( x−2 )( x−5 )=0 ( x−2 )( x−5 )=0

Solution

x=2,5 x=2,5

Exercise 2

( b+1 )( b−6 )=0 ( b+1 )( b−6 )=0

Exercise 3

( a+10 )( a−5 )=0 ( a+10 )( a−5 )=0

Solution

a=−10,5 a=−10,5

Exercise 4

( y−3 )( y−4 )=0 ( y−3 )( y−4 )=0

Exercise 5

( m−8 )( m+1 )=0 ( m−8 )( m+1 )=0

Solution

m=8,−1 m=8,−1

Exercise 6

( 4y+1 )( 2y+3 )=0 ( 4y+1 )( 2y+3 )=0

Exercise 7

( x+2 )( 3x−1 )=0 ( x+2 )( 3x−1 )=0

Solution

x=−2, 1 3 x=−2, 1 3

Exercise 8

( 5a−2 )( 3a−10 )=0 ( 5a−2 )( 3a−10 )=0

Exercise 9

x( 2x+3 )=0 x( 2x+3 )=0

Solution

x=0,− 3 2 x=0,− 3 2

Exercise 10

( a−5 ) 2 =0 ( a−5 ) 2 =0

Exercise 11

( y+3 ) 2 =0 ( y+3 ) 2 =0

Solution

y=−3 y=−3

Exercise 12

c 2 =36 c 2 =36

Exercise 13

16 y 2 −49=0 16 y 2 −49=0

Solution

y=± 7 4 y=± 7 4

Exercise 14

6 r 2 −36=0 6 r 2 −36=0

Exercise 15

a 2 +6a+8=0 a 2 +6a+8=0

Solution

a=−4,−2 a=−4,−2

Exercise 16

r 2 +7r+10=0 r 2 +7r+10=0

Exercise 17

s 2 −9s+8=0 s 2 −9s+8=0

Solution

s=1,8 s=1,8

Exercise 18

y 2 =−10y−9 y 2 =−10y−9

Exercise 19

11y−2=−6 y 2 11y−2=−6 y 2

Solution

y= 1 6 ,−2 y= 1 6 ,−2

Exercise 20

16 x 2 −3=−2x 16 x 2 −3=−2x

Exercise 21

m 2 =4m−4 m 2 =4m−4

Solution

m=2 m=2

Exercise 22

3( y 2 −8 )=−7y 3( y 2 −8 )=−7y

Exercise 23

a( 4b+7 )=0 a( 4b+7 )=0

Solution

a=0;  b=− 7 4 a=0;  b=− 7 4

Exercise 24

x 2 −64=0 x 2 −64=0

Exercise 25

m 2 −81=0 m 2 −81=0

Solution

m=±9 m=±9

Exercise 26

9 x 2 −25=0 9 x 2 −25=0

Exercise 27

5 a 2 −125=0 5 a 2 −125=0

Solution

a=±5 a=±5

Exercise 28

8 r 3 −6r=0 8 r 3 −6r=0

Exercise 29

m 2 −6m+5=0 m 2 −6m+5=0

Solution

m=5,1 m=5,1

Exercise 30

x 2 +2x−24=0 x 2 +2x−24=0

Exercise 31

x 2 +3x=28 x 2 +3x=28

Solution

x=−7,4 x=−7,4

Exercise 32

20 a 2 −3=7a 20 a 2 −3=7a

Exercise 33

2 y 2 −6y=8 2 y 2 −6y=8

Solution

y=4,−1 y=4,−1

Exercise 34

a 2 +2a=−1 a 2 +2a=−1

Exercise 35

2 r 2 =5−3r 2 r 2 =5−3r

Solution

r=− 5 2 ,1 r=− 5 2 ,1

Solving Quadratic Equations Using the Method of Extraction of Roots ((Reference))

For the following problems, solve the equations using extraction of roots.

Exercise 36

y 2 =81 y 2 =81

Exercise 37

a 2 =121 a 2 =121

Solution

a=±11 a=±11

Exercise 38

x 2 =35 x 2 =35

Exercise 39

m 2 =2 m 2 =2

Solution

m=± 2 m=± 2

Exercise 40

r 2 =1 r 2 =1

Exercise 41

s 2 −10=0 s 2 −10=0

Solution

s=± 10 s=± 10

Exercise 42

4 x 2 −64=0 4 x 2 −64=0

Exercise 43

−3 y 2 =−75 −3 y 2 =−75

Solution

y=±5 y=±5

Exercise 44

Solve y 2 =4 a 2 y 2 =4 a 2 for y. y.

Exercise 45

Solve m 2 =16 n 2 p 4 m 2 =16 n 2 p 4 for m. m.

Solution

m=±4n p 2 m=±4n p 2

Exercise 46

Solve x 2 =25 y 4 z 10 w 8 x 2 =25 y 4 z 10 w 8 for x. x.

Exercise 47

Solve x 2 − y 2 =0 x 2 − y 2 =0 for y. y.

Solution

y=±x y=±x

Exercise 48

Solve a 4 b 8 − x 6 y 12 z 2 =0 a 4 b 8 − x 6 y 12 z 2 =0 for a 2 . a 2 .

Exercise 49

( x−2 ) 2 =9 ( x−2 ) 2 =9

Solution

x=5,−1 x=5,−1

Exercise 50

( y+3 ) 2 =25 ( y+3 ) 2 =25

Exercise 51

( a+10 ) 2 =1 ( a+10 ) 2 =1

Solution

a=−11,−9 a=−11,−9

Exercise 52

( m+12 ) 2 =6 ( m+12 ) 2 =6

Exercise 53

( r−8 ) 2 =10 ( r−8 ) 2 =10

Solution

r=8± 10 r=8± 10

Exercise 54

( x−1 ) 2 =5 ( x−1 ) 2 =5

Exercise 55

( a−2 ) 2 =−2 ( a−2 ) 2 =−2

Solution

No real number solution.

Exercise 56

Solve ( x−2b ) 2 = b 2 ( x−2b ) 2 = b 2 for x x

Exercise 57

Solve ( y+6 ) 2 =a ( y+6 ) 2 =a for y. y.

Solution

y=−6± a y=−6± a

Exercise 58

Solve ( 2a−5 ) 2 =c ( 2a−5 ) 2 =c for a. a.

Exercise 59

Solve ( 3m−11 ) 2 =2 a 2 ( 3m−11 ) 2 =2 a 2 for m. m.

Solution

m= 11±a 2 3 m= 11±a 2 3

Solving Quadratic Equations Using the Method of Completing the Square ((Reference)) - Solving Quadratic Equations Using the Quadratic Formula ((Reference))

For the following problems, solve the equations by completing the square or by using the quadratic formula.

Exercise 60

y 2 −8y−12=0 y 2 −8y−12=0

Exercise 61

s 2 +2s−24=0 s 2 +2s−24=0

Solution

s=4,−6 s=4,−6

Exercise 62

a 2 +3a−9=0 a 2 +3a−9=0

Exercise 63

b 2 +b−8=0 b 2 +b−8=0

Solution

b= −1± 33 2 b= −1± 33 2

Exercise 64

3 x 2 −2x−1=0 3 x 2 −2x−1=0

Exercise 65

5 a 2 +2a−6=0 5 a 2 +2a−6=0

Solution

a= −1± 31 5 a= −1± 31 5

Exercise 66

a 2 =a+4 a 2 =a+4

Exercise 67

y 2 =2y+1 y 2 =2y+1

Solution

y=1± 2 y=1± 2

Exercise 68

m 2 −6=0 m 2 −6=0

Exercise 69

r 2 +2r=9 r 2 +2r=9

Solution

r=−1± 10 r=−1± 10

Exercise 70

3 p 2 +2p=7 3 p 2 +2p=7

Exercise 71

10 x 3 +2 x 2 −22x=0 10 x 3 +2 x 2 −22x=0

Solution

x=0, −1± 221 10 x=0, −1± 221 10

Exercise 72

6 r 3 +6 r 2 −3r=0 6 r 3 +6 r 2 −3r=0

Exercise 73

15 x 2 +2 x 3 =12 x 4 15 x 2 +2 x 3 =12 x 4

Solution

x=0, 1± 181 12 x=0, 1± 181 12

Exercise 74

6 x 3 −6x=−6 x 2 6 x 3 −6x=−6 x 2

Exercise 75

( x+3 )( x−4 )=3 ( x+3 )( x−4 )=3

Solution

x= 1± 61 2 x= 1± 61 2

Exercise 76

( y−1 )( y−2 )=6 ( y−1 )( y−2 )=6

Exercise 77

( a+3 )( a+4 )=−10 ( a+3 )( a+4 )=−10

Solution

No real number solution.

Exercise 78

( 2m+1 )( 3m−1 )=−2 ( 2m+1 )( 3m−1 )=−2

Exercise 79

( 5r+6 )( r−1 )=2 ( 5r+6 )( r−1 )=2

Solution

r= −1± 161 10 r= −1± 161 10

Exercise 80

4 x 2 +2x−3=3 x 2 +x+1 4 x 2 +2x−3=3 x 2 +x+1

Exercise 81

5 a 2 +5a+4=3 a 2 +2a+5 5 a 2 +5a+4=3 a 2 +2a+5

Solution

a= −3± 17 4 a= −3± 17 4

Exercise 82

( m+3 ) 2 =11 ( m+3 ) 2 =11

Exercise 83

( r−8 ) 2 =70 ( r−8 ) 2 =70

Solution

r=8± 70 r=8± 70

Exercise 84

( 2x+7 ) 2 =51 ( 2x+7 ) 2 =51

Applications ((Reference))

For the following problems, find the solution.

Exercise 85

The revenue R, R, in dollars, collected by a certain manufacturer of inner tubes is related to the number x x of inner tubes sold by R=1400−16x+3 x 2 . R=1400−16x+3 x 2 . How many inner tubes must be sold to produce a profit of $1361?

Solution

No solution.

Exercise 86

A study of the air quality in a particular city by an environmental group suggests that t t years from now the level of carbon monoxide, in parts per million, in the air will be A=0.8 t 2 +0.5t+3.3. A=0.8 t 2 +0.5t+3.3.
(a) What is the level, in parts per million, of carbon monoxide in the air now?
(b) How many years from now will the carbon monoxide level be at 6 parts per million?

Exercise 87

A contractor is to pour a concrete walkway around a community garden that is 15 feet wide and 50 feet long. The area of the walkway and garden is to be 924 square feet and of uniform width. How wide should the contractor make it?

Solution

x≈1.29 feet x≈1.29 feet

Exercise 88

A ball thrown vertically into the air has the equation of motion h=144+48t−16 t 2 h=144+48t−16 t 2
(a) How high is the ball at t=0? t=0?
(b) How high is the ball at t=1? t=1?
(c) When does the ball hit the ground?

Exercise 89

The length of a rectangle is 5 feet longer than three times its width. Find the dimensions if the area is to be 138 square feet.

Solution

w=6 w=6

Exercise 90

The area of a triangle is 28 square centimeters. The base is 3 cm longer than the height. Find both the length of the base and the height.

Exercise 91

The product of two consecutive integers is 210. Find them.

Solution

x=−15,−14, or 14,15 x=−15,−14, or 14,15

Exercise 92

The product of two consecutive negative integers is 272. Find them.

Exercise 93

A box with no top and a square base is to be made by cutting out 3-inch squares from each corner and folding up the sides of a piece of cardboard. The volume of the box is to be 25 cubic inches. What size should the piece of cardboard be?

Solution

x= 18+5 3 3 x= 18+5 3 3

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks