6.4 Completing the Square
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6.4 Completing the Square The Square Root Property
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6.4 Completing the Square. The Square Root Property. What does c equal to make the quadratic equation a prefect square. x 2 + 16x + c ;( x + ) 2. Square Root Property. Solve x 2 – 16 = 0 Factor into (x + 4)(x – 4) = 0 So the answers are 4, -4 This can be solve another way - PowerPoint PPT Presentation
Transcript of 6.4 Completing the Square
6.4 Completing the Square
The Square Root Property
What does c equal to make the quadratic equation a prefect square
x 2 + 16x + c ; ( x + )2
Square Root Property
Solve x2 – 16 = 0
Factor into (x + 4)(x – 4) = 0
So the answers are 4, -4
This can be solve another way
There are always two
answers. 4
16
162
x
x
x
Solve Using factoring and Square Root property
x2 + 16x + 64 = 36
(x + 8)(x + 8) = 36
(x + 8)2 = 36
Solve Using factoring and Square Root property
(x + 8)2 = 36
14 ,2
68
68
368
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x
x
x
Solve x2 – 10x + 25 = 12
Factor
125
125
2
2
x
x
Solve x2 – 10x + 25 = 12
Factor
325
325
125
125
2
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x
x
Solve x2 – 10x + 25 = 12
Factor
325
325
125
125
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x
x
x
325
325
x
x
Complete the Square
In case the quadratic equation is not a prefect square, we can force this to happen.
If a = 1, then we move c to the other side and add half of b squared to both side of the equation.
Complete the Square
If a = 1, then we move c to the other side and add half of b squared to both side of the equation.
22
222
2
2
22
22
0
bc
bx
bc
bbxx
cbxx
cbxx
Solve by Completing the Square
162
2122
44
124
0124
2
22
2
2
2
x
xx
xx
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6,2;42
42
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x
If a ≠ 1
abyDivide
cbxax
cbxax
2
2 0
22
222
2
22
22
a
b
a
c
a
bx
a
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a
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a
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a
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Solve 3x2 -2x – 1 = 0
3
1
3
2
123
0123
2
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xx
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Solve 3x2 -2x – 1 = 0
3
1
3
2
123
0123
2
2
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xx
9
4
9
1
9
3
3
1
3
1
3
1
3
2
2
1
3
2
2
222
x
xx
Solve 3x2 -2x – 1 = 0
3
1
3
2
123
0123
2
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3
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9
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1
9
4
9
1
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3
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1
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1
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1
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2
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2
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222
x
x
xx
Solve 3x2 -2x – 1 = 0
3
1
3
2
123
0123
2
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3
1 ;1
3
2
3
1
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2
9
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9
4
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1
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3
3
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3
1
3
1
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2
2
1
3
2
2
222
xx
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x
x
xx
Solve x2 + 2x + 3 = 0
Solve by completing the square.
132
22
32
032
22
2
2
xx
xx
xx
Solve x2 + 2x + 3 = 0
Solve by completing the square.
132
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32
032
22
2
2
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21
21 2
x
x
Solve x2 + 2x + 3 = 0
Solve by completing the square.
132
22
32
032
22
2
2
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21
21 2
x
x
21
21
ix
ix
Homework
Page 310 – 311
# 15 – 17 odd
25 – 47 odd
Homework
Page 310 – 311
# 14 – 18 even
24 – 40 even
