Completing the square
Completing the square of a
quadratic equation.
Example 1.
Colour edition.
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You were asked to
complete the
square of this
quadratic
equation:
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So we put the
equation into our
table.
1
2
3
4
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Highlight the part
of the equation
that contain
x2 and x only.
1
2
3
Do not highlight
the constant.
4
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Call this
expression as ‘p’.
1
2
3
4
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Rewrite 6x as
(2)(3) x.
1
2
3
4
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Rewrite 6x as
(2)(3) x.
1
2
3
4
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Rewrite 6x as
(2)(3) x.
1
2
3
4
We need to do this to apply the formula :
a b
2
a
2
2ab b
2
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Rewrite 6x as
(2)(3) x.
1
2
3
4
We need to do this to apply the formula :
a b
2
a
2
2ab b
2
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a=x
b=3
9

1
Add 32 to p.
2
Call this
expression : q
3
4
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1
Add 32 to p.
2
Call this
expression : q
3
4
a b
2
a
2
2ab b
2
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a=x
b=3
11

1
Add 32 to p.
2
Call this
expression : q
3
4
a b
2
a
2
2ab b
2
a=x
b=3
Now we can apply the above formula.
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a b
4
2
a2
2ab b 2
a=x
b=3
5
6
7
8
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a b
4
2
a2
2ab b 2
a=x
b=3
5
There! We applied
the formula.
6
7
8
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4
since
then
5
6
7
8
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4
since
5
then
6
7
8
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4
Simplify y.
5
-9 + 5 is 4
6
7
8
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Question :
Answer :
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