Beginning Algebra, 11th Edition

Step 4 Solve the equation by using the square root property.

or Square root property

or Take square roots.

or Subtract 2.

or

CHECK

x=- - 2 =-^42

9

2

x=

1

2

x=- 2 -

5

2

x=- 2 +

5

2

x+ 2 =-

5

2

x+ 2 =

5

2

x+ 2 =-

B

25

4

x+ 2 =

B

25

4

SECTION 9.2 Solving Quadratic Equations by Completing the Square 563

Let Let

0 = 0 ✓ True 0 = 0 ✓ True

1 + 8 - 9  0 81 - 72 - 9  0

4 a

81

4

4 a b - 72 - 9  0

1

4

b + 8 - 9  0

4 a- x=-^92.

9

2

b

2

+ 16 a-

9

2

4 a x=^12. b - 9  0

1

2

b

2

+ 16 a

1

2

b - 9  0

4 x^2 + 16 x- 9 = 0 4 x^2 + 16 x- 9 = 0

The two solutions, and check, so the solution set is NOW TRY

Solving a Quadratic Equation by Completing the Square

Solve

Step 1 Get 1 as the coefficient of the -term.

Divide by 2.

Step 2 Add to each side to get the variable terms on the left and the constant on

the right.

Add

Step 3 To complete the square, take half the coefficient of xand square it.

Add the result, to each side of the equation.

ax- Factor;^92 + 1649 =^7216 +^4916 =^12116.

7

4

b

2

=

121

16

x^2 -

7

2

x+

49

16

=

9

2

+

49

16

49

16 ,

c

1

2

a-

7

2

bd

2

= a-

7

4

b

2

=

49

16

9

x 2.

(^2) -^7
2
x=

9

2

9

2

x^2 -

7

2

x-

9

2

= 0

x^2

2 x^2 - 7 x- 9 =0.

EXAMPLE 5

21 - 29 , E- 29 , 21 F.

Be sure to add

to eachside.

(^4916)