Intermediate Algebra (11th edition)

SECTION 9.3 Equations Quadratic in Form 519

CAUTION A common error when solving problems like those in Examples 6

and 7is to stop too soon. Once you have solved for u, remember to substitute and

solve for the values of the original variable.

Complete solution available
on the Video Resources on DVD

Concept Check Write a sentence describing the first step you would take to solve each

equation. Do not actually solve.

1. 
   
   
   
   2. 
      
   
   
   
   


2. 1 x^2 +x 22 - 81 x^2 +x 2 + 12 = 0 4. 3 x= 216 - 10 x

21 +x+x= 5

14

x

=x- 5

5.Concept Check Study this incorrect

“solution.” WHAT WENT WRONG?

Square each side.

or

or

Solution set:

6.Concept Check Study this incorrect

“solution.”WHAT WENT WRONG?

Let

or

or

Solution set: E^12 , 1F

u= u= 1

1

2

2 u- 1 = 0 u - 1 = 0

12 u- 121 u- 12 = 0

u=x-1.

2 u^2 - 3 u+ 1 = 0

21 x- 122 - 31 x- 12 + 1 = 0

5 4, - 16

x= 4 x=- 1

x- 4 = 0 x + 1 = 0

1 x- 421 x+ 12 = 0

x^2 - 3 x- 4 = 0

x^2 = 3 x+ 4

x= 23 x+ 4

Solve each equation. Check your solutions. See Example 1.

7. 
   
   
   
   8. 
      
   
   
   
   

9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24. 1 -

1

3 x- 2

-

1

13 x- 222

1 - = 0

1

2 x+ 1

-

1

12 x+ 122

= 0

x

2 - x

+

2

x

= 5

6

p

= 2 +

p

p+ 1

1 +

2

3 z+ 2

=

15

13 z+ 222

3 =

1

t+ 2

+

2

1 t+ 222

4

3 x

-

1

21 x+ 12

= 1

3

2 x

-

1

21 x+ 22

= 1

4

3 - p

+

2

5 - p

=

26

15

2

x+ 1

+

3

x+ 2

=

7

2

2

m

+

3

m+ 9

=

11

4

1

x

+

2

x+ 2

=

17

35

1 +

2

x

=

3

x^2

3 -

1

t

=

2

t^2

4 -

7

r

-

2

r^2

1 - = 0

3

x

-

28

x^2

= 0

- 12

x

=x+ 8

14

x

=x- 5

9.3 EXERCISES