Easy Algebra Step-by-Step

Answer Key 229

1. x^2 − x − 6 = 0
   (x − 3) (x + 2) = 0
   x − 3 = 0 or x + 2 = 0
   x = 3 or x = −2


2. x^2 + 6x + 9 = −5 + 9
   (x + 3)^2 = 4
   x + 3 = ± 2
   x + 3 = 2 or x + 3 = −2
   x = −1 or x = −5


3. 3510

4

2

2

2

xx 5

x

55 x+

=−()−^5 ()^5 − ()^3 ()^1

() 3

x=^51 ±^3

6

4. x^2 − 6 = 8
   x^2 = 14
   x=± 14


5. x^2 − 3x+ 2 = 0

x=

−−( ) ( ) − ()( )

()

= −

(^33) )±−( (^41) ( 2
(^21) (
39 ± 8
2
2
x=
31 ±
2
x=^31 ±
2
x==
4
2
2 or x==
2
2
1

6. 9x^2 + 18 x − 17 = 0

x=

−± − ()()−

()

18 18 4 (

2 (

2

x=−±^18936

18

x=

−± (^1836) ()
18
x=−±^18626
18
x=
− 32 ± 6
3

7. 6x^2 − 12x + 7 = 0

x=

−()− ± ()− − ()()

()

=

±−

(^4) (
(^2) (
12 144 168
12
2
x=^12 ±−^24
12
There is no real solution because the
discriminant is negative.
Chapter 15 Solving Quadratic Equations
Exercise 15