Intermediate Algebra (11th edition)

512 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

Solve each equation. See Section 2.1.

61. 
    
    
    
    62. 
        
    
    
    
    

Solve each equation. See Section 8.6.

63. 22 x+ 6 =x- 1 64. 22 x+ 1 + 2 x+ 3 = 0

x

5

+

3 x

4

=- 19

3

4

x+

1

2

x=- 10

PREVIEW EXERCISES

OBJECTIVES OBJECTIVE 1 Solve an equation with fractions by writing it in quadratic

form.A variety of nonquadratic equations can be written in the form of a quadratic

equation and solved by using the methods of this chapter.

Solving an Equation with Fractions that Leads

to a Quadratic Equation

Solve

Clear fractions by multiplying each term by the least common denominator,

(Note that the domain must be restricted to )

Multiply by the LCD.

Distributive property

Distributive property

Combine like terms.

Standard form

Factor.

or Zero-factor property

or Solve for x.

The solution set is NOW TRY

OBJECTIVE 2 Use quadratic equations to solve applied problems.Some

distance-rate-time (or motion) problems lead to quadratic equations. We continue to

use the six-step problem-solving method from Section 2.3.

E

3

7 , 4F.

x=

3

7

7 x= 3 x= 4

7 x- 3 = 0 x - 4 = 0

17 x- 321 x- 42 = 0

7 x^2 - 31 x+ 12 = 0

24 x- 12 = 7 x^2 - 7 x

12 x- 12 + 12 x= 7 x^2 - 7 x

121 x- 12 + 12 x= 7 x 1 x- 12

12 x 1 x- 12

1

x

+ 12 x 1 x- 12

1

x- 1

= 12 x 1 x- 12

7

12

12 x 1 x- 12 a

1

x

+

1

x- 1

b = 12 x 1 x- 12 a

7

12

b

12 x 1 x- 12. xZ0,xZ 1.

1

x

+

1

x- 1

=

7

12

.

EXAMPLE 1

Equations Quadratic in Form

9.3

1 Solve an equation

with fractions by

writing it in

quadratic form.

2 Use quadratic

equations to solve

applied problems.

3 Solve an equation

with radicals by

writing it in

quadratic form.

4 Solve an equation

that is quadratic

in form by

substitution.

NOW TRY

EXERCISE 1

Solve.

2

x

+

3

x+ 2

= 1

NOW TRY ANSWER

1. 5 - 1, 4 6