Solving Equations Examples And Worksheet Page 4
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14A52
Appendix A
Review of Fundamental Concepts of Algebra
Quadratic Equations
A quadratic equation in is an equation that can be written in the general form
x
2
ax
bx
c
0
where
a,
b,
and are real numbers, with
c
a
0.
A quadratic equation in is also known
x
as a second-degree polynomial equation in
x.
You should be familiar with the following four methods of solving quadratic
equations.
Solving a Quadratic Equation
Factoring: If
ab
0,
then
a
0
or
b
0.
2
Example:
x
x
6
0
x
3 x
2
0
x
3
0
x
3
x
2
0
x
2
±
2
Square Root Principle: If
u
c,
where
c > 0,
then
u
c.
2
Example:
x
3
16
The Square Root Principle is
±
x
3
4
also referred to as extracting
±
square roots.
x
3
4
x
1
or
x
7
2
Completing the Square: If
x
bx
c,
then
2
2
b
b
2
b
2
x
bx
c
Add
to each side.
2
2
2
2
2
b
b
x
c
.
2
4
Example:
x
2
6x
5
2
6
2
2
2
x
6x
3
5
3
Add
to each side.
2
2
x
3
14
±
x
3
14
±
x
3
14
±
2
b
b
4ac
2
Quadratic Formula: If
ax
bx
c
0,
then
x
.
2a
2
Example:
2x
3x
1
0
You can solve every quadratic
±
equation by completing the
2
3
3
4
2
1
x
square or using the Quadratic
2
2
Formula.
±
3
17
4
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