NOTE We could have used factoring to solve the equation in Example 1.
Factor.or Zero-factor property
or Solve each equation.
or Same solutions as in Example 1
When solving quadratic equations, it is a good idea to try factoring first. If the poly-
nomial cannot be factored or if factoring is difficult, then use the quadratic formula.
Using the Quadratic Formula (Irrational Solutions)Solve
Write the equation in standard form as
Quadratic formulaSimplify.Factor.Lowest termsThe solution set is e. NOW TRY
2 23
2fx=
2 23
2
x=
4 A 2 23 B
4122
x = 248 = 216 # 23 = 423
8 423
8
x=
8 248
8
x=
8 264 - 16
8
x = a=4, b=-8, c= 1
- 1 - 82 21 - 822 - 4142112
2142
x=
- b 2 b^2 - 4 ac
2 a
4 x^2 - 8 x+ 1 =0.
4 x^2 = 8 x- 1.
EXAMPLE 2
x=-
1
2
x=
4
3
3 x= 4 2 x=- 1
3 x- 4 = 0 2 x+ 1 = 0
13 x- 4212 x+ 12 = 0
6 x^2 - 5 x- 4 = 0
SECTION 9.2 The Quadratic Formula 507
Factor first. Then
divide out the
common factor.CAUTION
1. Every quadratic equation must be expressed in standard form
before we begin to solve it,whether we use factoring or
the quadratic formula.
2. When writing solutions in lowest terms, be sure to FACTOR FIRST. Then
divide out the common factor,as shown in the last two steps in Example 2.
ax^2 bxc 0
NOW TRY
EXERCISE 2
Solve. 3 x^2 + 1 =- 5 x
NOW TRY ANSWER
- e
- 5 213
6
f
- 5 213
This is a
key step.