Completing the square v002

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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:

3

1

2

3

4

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So we put the equation into our table.

4

1

2

3

4


Highlight the part of the equation that contain x2 and x only.

Do not highlight the constant.

5

1

2

3

4


Call this expression as ‘p’.

6

1

2

3

4


Rewrite 6x as (2)(3) x.

7

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2

3

4



8

1

2

3

4



We need to do this to apply the formula :

222 2 bababa

9

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2

3

4



We need to do this to apply the formula :

222 2 bababa a = xb = 3

10

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2

3

4


Add 32 to p.

Call this expression : q

11

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2

3

4


Add 32 to p.


222 2 bababa a = xb = 3

12

1

2

3

4


Add 32 to p.


222 2 bababa a = xb = 3

Now we can apply the above formula.

13

4

5

6

7

8


222 2 bababa

a = xb = 3

14

4

5

6

7

8


222 2 bababa

a = xb = 3

There! We applied the formula.

15

4

5

6

7

8


since

then

16

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5

6

7

8


since

then

17

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5

6

7

8


Simplify y. -9 + 5 is 4

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Completing the square v002