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§ 11.3
Solving Equations by
Using Quadratic Methods
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View Full Document MartinGay,
Beginning and Intermediate Algebra, 4ed
2
Solving Quadratic Equations
Solving a Quadratic Equation
1)
If the equation is in the form (
ax
+
b
)
2
=
c
, use the
square root property and solve.
If not, go to Step 2.
2)
Write the equation in standard form:
ax
2
+
bx
+
c
= 0.
3)
Try to solve the equation by the factoring method.
If
not possible, go to Step 4.
4)
Solve the equation by
the quadratic formula.
MartinGay,
Beginning and Intermediate Algebra, 4ed
3
Note that the directions on the previous slide
did NOT include completing the square.
Completing the square often involves more
complicated computations with fractions,
which can be avoided by using the quadratic
formula.
Solving Quadratic Equations
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View Full Document MartinGay,
Beginning and Intermediate Algebra, 4ed
4
Solve 12
x
= 4
x
2
+ 4.
0 = 4
x
2
– 12
x
+ 4
0 = 4(
x
2
– 3
x
+ 1)
Let
a
= 1,
b
= –3,
c
= 1
=


±
=
)
1
(
2
)
1
)(
1
(
4
)
3
(
3
2
x
=

±
2
4
9
3
2
5
3
±
Solving Quadratic Equations
Example:
MartinGay,
Beginning and Intermediate Algebra, 4ed
5
Solve the following quadratic equation.
0
2
1
8
5
2
=

+
m
m
0
)
2
)(
2
5
(
=
+

m
m
0
2
0
2
5
=
+
=

m
m
or
2
5
2

=
=
m
m
or
0
4
8
5
2
=

+
m
m
(multiply both sides by 8)
Solving Quadratic Equations
Example:
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Beginning and Intermediate Algebra, 4ed
6
The steps we detailed in solving quadratic equations
will only work if the equation is in an obviously
recognizable form.
Sometimes, we may have to alter the form of an
equation to get it into quadratic form.
This might involve substitution into the equation,
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This note was uploaded on 11/04/2011 for the course MATH 103 taught by Professor Alraban during the Fall '10 term at Montgomery College.
 Fall '10
 Alraban
 Math, Equations

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