Beginning Algebra, 11th Edition

CHAPTER 9 Summary 589

Step 3 Take half the coefficient of x, square it, and add
the square to each side of the equation. Factor
the variable side and combine terms on the
other side.

Step 4 Use the square root property to solve the
equation.

Add

Factor. Add.

or

or

or

or

The solution set is e

• 2  26
  2

f.

x=

• 2 - 26
  2

x=

• 2 + 26
  2

x=- 1 -

26

2

x=- 1 +

26

2

x+ 1 =-

26

2

x+ 1 =

26

2

x+ 1 =-

B

3

2

x+ 1 =

B

3

2

1 x+ 122 =

3

2

x^2 + 2 x+ 1 = C 21122 D^2 = 12 =1.

1

2

+ 1

9.3 Solving Quadratic Equations by the

Quadratic Formula

Quadratic Formula
The solutions of are

The discriminant of the quadratic equation is

b^2  4 ac.

x

b 2 b^2  4 ac

2 a

.

ax^2 +bx+c=0,aZ0,

Solve

Simplify.

Factor out 2.

Divide out 2.

The solution set is e.

2  210

3

f

x=

2  210

3

x=

(^2) A 2  (^210) B
2 # 3
= 2210
240 = 24 # 10
x=
4  2210
6
x=
4  240
6
c=- 2
a=3,b=-4,
x=

• 1 - 42  21 - 422 - 41321 - 22
  2132

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

CONCEPTS EXAMPLES

9.4 Complex Numbers
The imaginary unit is i, where

, and thus,

For the positive number b, 2 bi 2 b.

i 2  1 i^2 1.

2 - 19 =i 219

Addition
Add complex numbers by adding the real parts and
adding the imaginary parts.

Add.

=- 6 + 8 i

= 13 - 92 + 16 + 22 i

13 + 6 i 2 + 1 - 9 + 2 i 2

(continued)