Solving Equations Examples And Worksheet Page 7
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14A55
Appendix A.5
Solving Equations
Example 8
The Quadratic Formula: Two Distinct Solutions
WARNING / CAUTION
2
When using the Quadratic
Use the Quadratic Formula to solve
x
3x
9.
Formula, remember that before
Solution
the formula can be applied, you
2
x
3x
9
must first write the quadratic
Write original equation.
equation in general form.
2
x
3x
9
0
Write in general form.
±
2
b
b
4ac
x
Quadratic Formula
2a
±
2
3
3
4
1
9
Substitute
a
1,
x
b
3,
and c
9.
2
1
±
3
45
x
Simplify.
2
±
3
3 5
x
Simplify.
2
The equation has two solutions:
3
3 5
3
3 5
x
and
x
.
2
2
Check these in the original equation.
Now try Exercise 87.
Example 9
The Quadratic Formula: One Solution
2
Use the Quadratic Formula to solve
8x
24x
18
0.
Solution
2
8x
24x
18
0
Write original equation.
Divide out common
2
4x
12x
9
0
factor of 2.
±
2
b
b
4ac
x
Quadratic Formula
2a
±
2
12
12
4
4 9
Substitute
a
4,
x
b
12,
and c
9.
2
4
±
12
0
3
x
Simplify.
8
2
3
This quadratic equation has only one solution:
x
.
Check this in the original
2
equation.
Now try Exercise 91.
Note that Example 9 could have been solved without first dividing out a common
factor of 2. Substituting
a
8,
b
24,
and
c
18
into the Quadratic Formula
produces the same result.
ADVERTISEMENT
0 votes
Related Articles
Related forms
2.4 Write Equations Of Lines Examples And Worksheet - Chapter 2, Linear Equations And Functions
Education
Chapter 5 Solving Systems Of Linear Equations - 5.5 Solving Equations By Graphing Worksheet
Education
Lesson 3.3, 3.4, And 3.5: Adding, Subtracting, And Multiplying Integers Examples And Worksheets
Education
Capacity And Weight In The Customary System Examples And Worksheet - Chapter 8 Systems Of Measurement
Education
Related Categories
Parent category: Education