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14.4B completing the square
14.4B completing the square
You need your notebook and Ipad
1 / 11
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Slide 1:
Slide
Wiskunde
Middelbare school
vmbo lwoo, havo
Leerjaar 3
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14.4B completing the square
You need your notebook and Ipad
Slide 1 - Slide
Solving quadratic equations
x
2
+
1
3
x
+
3
6
=
0
Slide 2 - Slide
Solving quadratic equations
(
x
+
5
)
2
=
0
Slide 3 - Slide
Solving quadratic equations
(
4
x
−
2
0
)
2
=
0
Slide 4 - Slide
Solving quadratic equations
(
x
+
8
)
2
=
1
0
0
Slide 5 - Slide
Solving quadratic equations
(
x
+
8
)
2
=
(
x
+
9
)
2
=
(
x
+
1
0
)
2
=
Slide 6 - Slide
Solving quadratic equations
x
2
+
1
4
x
+
5
0
=
Slide 7 - Slide
Note 14.4B: Completing the square
You can solve every quadratic equation of the form:
by completing the square.
First step: Changing to
Second step: solving the equation
x
2
+
b
x
+
c
=
0
x
2
+
b
x
+
c
=
0
(
x
+
2
b
)
2
+
c
−
(
2
b
)
2
=
0
Slide 8 - Slide
Note 14.4B: Completing the square
Example: Solve:
First step:
Solving the equation:
or
or
x
2
+
1
8
x
+
1
7
=
0
(
x
+
2
1
8
)
2
+
1
7
−
(
2
1
8
)
2
=
0
(
x
+
9
)
2
+
1
7
−
9
2
=
0
(
x
+
9
)
2
+
1
7
−
8
1
=
0
(
x
+
9
)
2
−
6
4
=
0
(
x
+
9
)
2
=
6
4
x
+
9
=
8
x
+
9
=
−
8
x
=
−
1
x
=
−
1
7
Slide 9 - Slide
Solve by completing the square
x
2
+
1
2
x
−
1
3
=
0
Slide 10 - Slide
Bettermarks
Work on 14.4B
Raise your finger if you have any questions or when you're finished
Slide 11 - Slide
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