Elementary Algebra

Problem 1

Solve by factoring and then solve by extracting roots. Check answers.
$$
x 2-36=0
$$

Teresa Fuston

Numerade Educator

Problem 2

Solve by factoring and then solve by extracting roots. Check answers.
$$
x 2-81=0
$$

Teresa Fuston

Numerade Educator

01:11

Problem 3

Solve by factoring and then solve by extracting roots. Check answers.
$$
4 y 2-9=0
$$

Teresa Fuston

Numerade Educator

Problem 4

Solve by factoring and then solve by extracting roots. Check answers.
$$
9 y 2-25=0
$$

Teresa Fuston

Numerade Educator

02:17

Problem 5

Solve by factoring and then solve by extracting roots. Check answers.
$$
(x-2) 2-1=0
$$

Teresa Fuston

Numerade Educator

01:35

Problem 6

Solve by factoring and then solve by extracting roots. Check answers.
$$
(x+1) 2-4=0
$$

Teresa Fuston

Numerade Educator

02:40

Problem 7

Solve by factoring and then solve by extracting roots. Check answers.
$$
4(y-2) 2-9=0
$$

Teresa Fuston

Numerade Educator

02:16

Problem 8

Solve by factoring and then solve by extracting roots. Check answers.
$$
9(y+1) 2-4=0
$$

Teresa Fuston

Numerade Educator

01:24

Problem 9

Solve by factoring and then solve by extracting roots. Check answers.
$$
-3(t-1) 2+12=0
$$

Teresa Fuston

Numerade Educator

01:26

Problem 10

Solve by factoring and then solve by extracting roots. Check answers.
$$
-2(t+1) 2+8=0
$$

Teresa Fuston

Numerade Educator

01:18

Problem 11

Solve by factoring and then solve by extracting roots. Check answers.
$$
(x-5) 2-25=0
$$

Teresa Fuston

Numerade Educator

01:24

Problem 12

Solve by factoring and then solve by extracting roots. Check answers.
$$
(x+2) 2-4=0
$$

Teresa Fuston

Numerade Educator

Problem 13

Solve by extracting the roots.
$$
x_{2}=16
$$

Teresa Fuston

Numerade Educator

Problem 14

Solve by extracting the roots.
$$
x_{2}=1
$$

Teresa Fuston

Numerade Educator

Problem 15

Solve by extracting the roots.
$$
y 2=9
$$

Teresa Fuston

Numerade Educator

Problem 16

Solve by extracting the roots.
$$
y 2=64
$$

Teresa Fuston

Numerade Educator

Problem 17

Solve by extracting the roots.
$$
x 2=14
$$

Teresa Fuston

Numerade Educator

Problem 18

Solve by extracting the roots.
$$
x 2=19
$$

Teresa Fuston

Numerade Educator

Problem 19

Solve by extracting the roots.
$$
y 2=0.25
$$

Teresa Fuston

Numerade Educator

01:14

Problem 20

Solve by extracting the roots.
$$
y 2=0.04
$$

Teresa Fuston

Numerade Educator

Problem 21

Solve by extracting the roots.
$$
x_{2}=12
$$

Teresa Fuston

Numerade Educator

Problem 22

Solve by extracting the roots.
$$
x 2=18
$$

Teresa Fuston

Numerade Educator

Problem 23

Solve by extracting the roots.
$$
16 x 2=9
$$

Teresa Fuston

Numerade Educator

Problem 24

Solve by extracting the roots.
$$
4 x 2=25
$$

Teresa Fuston

Numerade Educator

Problem 25

Solve by extracting the roots.
$$
2 t 2=1
$$

Teresa Fuston

Numerade Educator

Problem 26

Solve by extracting the roots.
$$
3 t 2=2
$$

Teresa Fuston

Numerade Educator

Problem 27

Solve by extracting the roots.
$$
x_{2}-100=0
$$

Teresa Fuston

Numerade Educator

01:00

Problem 28

Solve by extracting the roots.
$$
x_{2}-121=0
$$

Teresa Fuston

Numerade Educator

Problem 29

Solve by extracting the roots.
$$
y 2+4=0
$$

Teresa Fuston

Numerade Educator

Problem 30

Solve by extracting the roots.
$$
y 2+1=0
$$

Teresa Fuston

Numerade Educator

Problem 31

Solve by extracting the roots.
$$
x 2-49=0
$$

Teresa Fuston

Numerade Educator

01:10

Problem 32

Solve by extracting the roots.
$$
x_{2}-925=0
$$

Teresa Fuston

Numerade Educator

01:16

Problem 33

Solve by extracting the roots.
$$
y 2-0.09=0
$$

Teresa Fuston

Numerade Educator

Problem 34

Solve by extracting the roots.
$$
y 2-0.81=0
$$

Teresa Fuston

Numerade Educator

Problem 35

Solve by extracting the roots.
$$
x_{2}-7=0
$$

Teresa Fuston

Numerade Educator

Problem 36

Solve by extracting the roots.
$$
x_{2}-2=0
$$

Teresa Fuston

Numerade Educator

Problem 37

Solve by extracting the roots.
$$
x_{2}-8=0
$$

Teresa Fuston

Numerade Educator

Problem 38

Solve by extracting the roots.
$$
t 2-18=0
$$

Teresa Fuston

Numerade Educator

Problem 39

Solve by extracting the roots.
$$
x_{2}+8=0
$$

Teresa Fuston

Numerade Educator

Problem 40

Solve by extracting the roots.
$$
x_{2}+125=0
$$

Teresa Fuston

Numerade Educator

Problem 41

Solve by extracting the roots.
$$
16 x 2-27=0
$$

Teresa Fuston

Numerade Educator

Problem 42

Solve by extracting the roots.
$$
9 x 2-8=0
$$

Teresa Fuston

Numerade Educator

Problem 43

Solve by extracting the roots.
$$
2 y 2-3=0
$$

Teresa Fuston

Numerade Educator

Problem 44

Solve by extracting the roots.
$$
5 y 2-2=0
$$

Teresa Fuston

Numerade Educator

01:07

Problem 45

Solve by extracting the roots.
$$
3 x 2-1=0
$$

Teresa Fuston

Numerade Educator

Problem 46

Solve by extracting the roots.
$$
6 x 2-3=0
$$

Teresa Fuston

Numerade Educator

Problem 47

Solve by extracting the roots.
$$
(x+7) 2-4=0
$$

Teresa Fuston

Numerade Educator

Problem 48

Solve by extracting the roots.
$$
(x+9) 2-36=0
$$

Teresa Fuston

Numerade Educator

Problem 49

Solve by extracting the roots.
$$
(2 y-3) 2-81=0
$$

Teresa Fuston

Numerade Educator

Problem 50

Solve by extracting the roots.
$$
(2 y+1) 2-25=0
$$

Teresa Fuston

Numerade Educator

Problem 51

Solve by extracting the roots.
$$
(x-5) 2-20=0
$$

Teresa Fuston

Numerade Educator

Problem 52

Solve by extracting the roots.
$$
(x+1) 2-28=0
$$

Teresa Fuston

Numerade Educator

Problem 53

Solve by extracting the roots.
$$
(3 t+2) 2-6=0
$$

Teresa Fuston

Numerade Educator

Problem 54

Solve by extracting the roots.
$$
(3 t-5) 2-10=0
$$

Teresa Fuston

Numerade Educator

01:07

Problem 55

Solve by extracting the roots.
$$
4(y+2) 2-3=0
$$

Teresa Fuston

Numerade Educator

Problem 56

Solve by extracting the roots.
$$
9(y-7) 2-5=0
$$

Teresa Fuston

Numerade Educator

01:43

Problem 57

Solve by extracting the roots.
$$
4(3 x+1) 2-27=0
$$

Teresa Fuston

Numerade Educator

01:16

Problem 58

Solve by extracting the roots.
$$
9(2 x-3) 2-8=0
$$

Teresa Fuston

Numerade Educator

Problem 59

Solve by extracting the roots.
$$
2(3 x-1) 2+3=0
$$

Teresa Fuston

Numerade Educator

01:25

Problem 60

Solve by extracting the roots.
$$
5(2 x-1) 2-3=0
$$

Teresa Fuston

Numerade Educator

01:19

Problem 61

Solve by extracting the roots.
$$
3(y-23) 2-32=0
$$

Teresa Fuston

Numerade Educator

01:14

Problem 62

Solve by extracting the roots.
$$
2(3 y-13) 2-52=0
$$

Teresa Fuston

Numerade Educator

Problem 63

Find a quadratic equation in standard form with the following solutions.
$$
\pm 7
$$

Teresa Fuston

Numerade Educator

Problem 64

Find a quadratic equation in standard form with the following solutions.
$$
\pm 13
$$

Teresa Fuston

Numerade Educator

Problem 65

Find a quadratic equation in standard form with the following solutions.
$$
\pm 7 \sqrt{ }
$$

Teresa Fuston

Numerade Educator

Problem 66

Find a quadratic equation in standard form with the following solutions.
$$
\pm 3 \sqrt{ }
$$

Teresa Fuston

Numerade Educator

Problem 67

Find a quadratic equation in standard form with the following solutions.
$$
\pm 35 \sqrt{ }
$$

Teresa Fuston

Numerade Educator

Problem 68

Find a quadratic equation in standard form with the following solutions.
$$
\pm 52 \sqrt{ }
$$

Teresa Fuston

Numerade Educator

Problem 69

Find a quadratic equation in standard form with the following solutions.
$$
1 \pm 2 \sqrt{ }
$$

Teresa Fuston

Numerade Educator

Problem 70

Find a quadratic equation in standard form with the following solutions.
$$
2 \pm 3 \sqrt{ }
$$

Teresa Fuston

Numerade Educator

Problem 71

Solve and round off the solutions to the nearest hundredth.
$$
9 x(x+2)=18 x+1
$$

Teresa Fuston

Numerade Educator

Problem 72

Solve and round off the solutions to the nearest hundredth.
$$
x_{2}=10(x 2-2)-5
$$

Teresa Fuston

Numerade Educator

01:28

Problem 73

Solve and round off the solutions to the nearest hundredth.
$$
(x+3)(x-7)=11-4 x
$$

Teresa Fuston

Numerade Educator

01:19

Problem 74

Solve and round off the solutions to the nearest hundredth.
$$
(x-4)(x-3)=66-7 x
$$

Teresa Fuston

Numerade Educator

01:16

Problem 75

Solve and round off the solutions to the nearest hundredth.
$$
(x-2) 2=67-4 x
$$

Teresa Fuston

Numerade Educator

01:06

Problem 76

Solve and round off the solutions to the nearest hundredth.
$$
(x+3) 2=6 x+59
$$

Teresa Fuston

Numerade Educator

01:49

Problem 77

Solve and round off the solutions to the nearest hundredth.
$$
(2 x+1)(x+3)-(x+7)=(x+3) 2
$$

Teresa Fuston

Numerade Educator

01:33

Problem 78

Solve and round off the solutions to the nearest hundredth.
$$
(3 x-1)(x+4)=2 x(x+6)-(x-3)
$$

Teresa Fuston

Numerade Educator

Problem 79

Set up an algebraic equation and use it to solve the following.
If 9 is subtracted from 4 times the square of a number, then the result is 3 . Find the number.

Teresa Fuston

Numerade Educator

Problem 80

Set up an algebraic equation and use it to solve the following.
If 20 is subtracted from the square of a number, then the result is $4 .$ Find the number.

Teresa Fuston

Numerade Educator

Problem 81

Set up an algebraic equation and use it to solve the following.
If 1 is added to 3 times the square of a number, then the result is 2 . Find the number.

Teresa Fuston

Numerade Educator

Problem 82

Set up an algebraic equation and use it to solve the following.
If 3 is added to 2 times the square of a number, then the result is 12 . Find the number.

Teresa Fuston

Numerade Educator

Problem 83

Set up an algebraic equation and use it to solve the following.
If a square has an area of 8 square centimeters, then find the length of each side.

Teresa Fuston

Numerade Educator

01:17

Problem 84

Set up an algebraic equation and use it to solve the following.
If a circle has an area of $32 \pi$ square centimeters, then find the length of the radius.

Teresa Fuston

Numerade Educator

01:34

Set up an algebraic equation and use it to solve the following.
The volume of a right circular cone is $36 \pi$ cubic centimeters when the height is 6 centimeters. Find the radius of the cone. (The volume of a right circular cone is given by $V=13 \pi r 2 h .)$

Teresa Fuston

Numerade Educator

01:11

Problem 86

Set up an algebraic equation and use it to solve the following.
The surface area of a sphere is $75 \pi$ square centimeters. Find the radius of the sphere. (The surface area of a sphere is given by $S A=4 \pi r 2 .$

Teresa Fuston

Numerade Educator

01:19

Problem 87

Set up an algebraic equation and use it to solve the following.
The length of a rectangle is 6 times its width. If the area is 96 square inches, then find the dimensions of the rectangle.

Teresa Fuston

Numerade Educator

Problem 88

Set up an algebraic equation and use it to solve the following.
The base of a triangle is twice its height. If the area is 16 square centimeters, then find the length of its base.

Teresa Fuston

Numerade Educator

01:34

Problem 89

Set up an algebraic equation and use it to solve the following.
A square has an area of 36 square units. By what equal amount will the sides have to be increased to create a square with double the given area?

Teresa Fuston

Numerade Educator

01:47

Problem 90

A circle has an area of $25 \pi$ square units. By what amount will the radius have to be increased to create a circle with double the given area?

Teresa Fuston

Numerade Educator

Problem 91

If the sides of a square measure 1 unit, then find the length of the diagonal.

Teresa Fuston

Numerade Educator

01:06

Problem 92

If the sides of a square measure 2 units, then find the length of the diagonal.

Teresa Fuston

Numerade Educator

Problem 93

The diagonal of a square measures 5 inches. Find the length of each side.

Teresa Fuston

Numerade Educator

01:00

Problem 94

The diagonal of a square measures 3 inches. Find the length of each side.

Teresa Fuston

Numerade Educator

01:22

Problem 95

The length of a rectangle is twice its width. If the diagonal measures 10 feet, then find the dimensions of the rectangle.

Teresa Fuston

Numerade Educator

01:39

Problem 96

The length of a rectangle is twice its width. If the diagonal measures 8 feet, then find the dimensions of the rectangle.

Teresa Fuston

Numerade Educator

01:44

Problem 97

The length of a rectangle is 3 times its width. If the diagonal measures 5 meters, then find the dimensions of the rectangle.

Teresa Fuston

Numerade Educator

01:18

Problem 98

The length of a rectangle is 3 times its width. If the diagonal measures 2 feet, then find the dimensions of the rectangle.

Teresa Fuston

Numerade Educator

01:14

Problem 99

The height in feet of an object dropped from a 9-foot ladder is given by $h(t)=-16 t 2+9,$ where $t$ represents the time in seconds after the object has been dropped. How long does it take the object to hit the ground? (Hint: The height is 0 when the object hits the ground.)

Teresa Fuston

Numerade Educator

01:06

Problem 100

The height in feet of an object dropped from a 20-foot platform is given by $h(t)=-16 t 2+20,$ where $t$ represents the time in seconds after the object has been dropped. How long does it take the object to hit the ground?

Teresa Fuston

Numerade Educator

02:02

Problem 101

The height in feet of an object dropped from the top of a 144 -foot building is given by $h(t)=-16 t 2+144,$ where $t$ is measured in seconds.
a. How long will it take to reach half of the distance to the ground, 72 feet?
b. How long will it take to travel the rest of the distance to the ground?

Teresa Fuston

Numerade Educator

01:50

Problem 102

The height in feet of an object dropped from an airplane at 1,600 feet is given by $h(t)=-16 t 2+1,600,$ where $t$ is in seconds.
a. How long will it take to reach half of the distance to the ground?
b. How long will it take to travel the rest of the distance to the ground? Round off to the nearest hundredth of a second.

Teresa Fuston

Numerade Educator