Chapter 10 QuadratiC EQuations 369

EXAMPLES
Solve the quadratic equation with the quadratic formula.

2 x^2 + 3 x+ 1 = 0

We begin by observing a, b, and c: a = 2 b = 3 c = 1.

x=−± − =−± −

=−± =−+ −−

33421

22

398

4

31

4

31

4

31

4

()^2 ()()

()

, ==−−^2 =− −

4

4

4

1

2

,, 1

Solve the quadratic equation with the quadratic formula.

x^2 −x− 1 = 0 a= 1 b=− 1 c=− 1

x=−− ±−−−

= ±−− = ±+= ±

() () ()()

()

()

1141 1

21

114

2

114

2

15

2

22

15

2

15

2

= +−,

Solve the quadratic equation with the quadratic formula.

x^2 − 18 = 0 a = 1 b = 0 c=− 18

x=−± −−=±−−

=± =±⋅=±

0041 18

21

072

2

72

2

36 2

2

62

(^2) ()()
()
()
22
=± =−32 32 32,
Solve the quadratic equation with the quadratic formula.
2 x^2 + 6 x= 5
Rewrite as 26 xx^2 +  –  50 =  a = 2 b = 6 c = –5
x=−± −−^66425 =−± −− =−± =−± ⋅
22
63640
4
676
4
(^2) ()() 641
()
() 99
4

−± (^6219) = −± =−± =−+ −−
4
23 19
4
319
2
319
2
319
2
() ,
EXAMPLES
Solve the quadratic equation with the quadratic formula.
2
EXAMPLES
Solve the quadratic equation with the quadratic formula.