Step 4

Step 5

Step 6 or

or

or Add

or

Check that the solution set is e. NOW TRY

• 5  229
  2
  f

a

c

b

c=

ab

x= c

- 5 - 229

2

x=

- 5 + 229

2

x=- -^52.

5

2

-

229

2

x=-

5

2

+

229

2

2

a

b=

a

x+ b

5

2

=-

229

2

x+

5

2

=

229

2

x+

5

2

=-

B

29

4

x+

5

2

=

B

29

4

ax+

5

2

b

2

=

29

4

x^2 + 5 x+

25

4

= 1 +

25

4

SECTION 9.1 The Square Root Property and Completing the Square 501

Factor on the left.

Add on the right.

Add the square to each

side of the equation.

Square root

property

Solving a Quadratic Equation by Completing the Square

Solve

Divide each side by 2 to get 1 as the coefficient of the second-degree term.

Step 1

Step 2

Step 3

Step 4

Step 5

or Step 6

or Add 1.

or

Add the two terms in each solution as follows.

Check that the solution set is e. NOW TRY

2  214

2

f

1 -

214

2

=

2

2

-

214

2

=

2 - 214

2

1 + 1 =^22

214

2

=

2

2

+

214

2

=

2 + 214

2

214

= 2

27

22

#^22

22

(^27) =
22

B
7
2

x= 1 -

214

2

x= 1 +

214

2

x= 1 -

B

7

2

x= 1 +

B

7

2

x- 1 =-

B

7

2

x- 1 =

B

7

2

1 x- 122 =

7

2

x^2 - 2 x+ 1 =

5

2

+ 1

c

1

2

1 - 2 2d

2

= 1 - 122 = 1

x^2 - 2 x=

5

2

x^2 - 2 x-

5

2

= 0

2 x^2 - 4 x- 5 =0.

EXAMPLE 8 1 a 12

NOW TRY
EXERCISE 7
Solve .x^2 +x- 3 = 0

NOW TRY ANSWERS

7. 
   

8.e

• 6  251
  3
  f

e

• 1  213
  2
  f

NOW TRY
EXERCISE 8
Solve. 3 x^2 + 12 x- 5 = 0