Beginning Algebra, 11th Edition

CHECKSubstitute each solution in the original equation.

Let Let

Subtract. Subtract.

✓ True ✓ True

The solution set is

(b)

or Square root property

or Add 1.

CHECK ✓ Let

✓ Let

The solution set is E 1 + 26 , 1- 26 F,or E 1  26 F. NOW TRY

(^) A 1 - 26 - (^1) B x= 1 - 26.
2
= A- (^26) B
2
= 6
A 1 + 26 - 1 B x= 1 + 26.
2
= A 26 B
2
= 6
x= 1 + 26 x = 1 - 26
x- 1 = 26 x - 1 =- 26
1 x- 122 = 6

5 - 1, 7 6.

16 = 16 16 = 16

42  16 1 - 422  16

1 7 - 322  16 x=7. 1 - 1 - 322  16 x=-1.

1 x- 322 = 16 1 x- 322 = 16

556 CHAPTER 9 Quadratic Equations

NOW TRY

1 ab 22 =a^2 b^2

CAUTION The solutions in Example 4are fractions that cannot be simplified,

since 3 is nota common factor in the numerator.

Recognizing a Quadratic Equation with No Real Solutions

Solve

Because the square root of is not a real number, the solution set is

NOW TRY

- 9 0.

1 x+ 322 =- 9.

EXAMPLE 5

Solving a Quadratic Equation of the Form

Solve

or Square root property

or

or Add 2.

or Divide by 3.

CHECK Let.

Multiply.

Subtract.

✓ True

The check of the other solution is similar. The solution set is e

2  323

3

f.

27 = 27

A 323 B

(^2) 
27

A 2 + 323 - 2 B

(^2) 
27
2 + 323
a 3 r= 3
#^2 +^323
3

• 2 b

2

 27

r=

2 - 323

3

r=

2 + 323

3

3 r= 2 + 323 3 r= 2 - 323

3 r- 2 = 323 3 r- 2 =- 323 227 = 29 # 23 = 323

3 r- 2 = 227 3 r- 2 =- 227

13 r- 222 = 27

13 r- 222 =27.

EXAMPLE 4 1 axb 22 k

NOW TRY
EXERCISE 3
Solve 1 x- 222 =32.

NOW TRY ANSWERS

3. 
   
   
   
   4. 
      
   
   
   
   


4. 0

e^4 ^522

2

E^2 ^422 F f

NOW TRY
EXERCISE 4
Solve 12 t- 422 =50.

NOW TRY
EXERCISE 5
Solve 12 x+ 122 =-5.

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