Solving by Factoring

Factored

100

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

x=3, -2

200

(2x+1)(3x-4)=0

x=-1/2, 4/3

300

2(x+3)=0

x=-3

400

x(2x+7)=0

x=0, -7/2

500

4x(3x-6)=0

x=0, 2

Zero-ed

100

x²-6x-7=0

x=7, -1

200

x²-18x-40=0

x=20, -2

300

x²-1=0

x=1, -1

400

3x²-7x+2=0

x=2, 1/3

500

-2x²-x+1=0

x=-1, 1/2

It's Complicated...

100

x²+3=4x

x=3, 1

200

3x²+1=-4x

x=-1, -1/3

300

x²+2x+20=-10x+9

x=-11, -1

400

6x²=3x

x=0, 1/2

500

4x²=9

x=3/2, -3/2

Proportions

100

x/9=16/x

x=12, -12

200

2x/-2 =2/x-3

x=2, 1

300

x+5/6=6/x+5

x=1, -11

400

(x-3)/-x = 2/(x+2)

x=-3, 2

500

(2x+1)/x = (x+11)/(x+3)

x=3, 1

Word Problems

100

16 times a number squared is 81. What is the larger possible number? 

9/4

200

The length of a rectangle is 2 shorter than the width. If the area is 8 square units, what is the length? 

2 units

300

Double a number squared is equal to three times that number. What is the smaller possibility? 

0

400

The area of a square is 144 square units. What is the side length of the square? 

12 units

500

Two negative consecutive numbers multiply to 30. What are the numbers? 

-5 & -6