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Completing the square
Completing the square of a
quadratic equation.

Example 1.
Colour edition.

singaporestudent.com

1
You were asked to
complete the
square of this
quadratic
equation:

singaporestudent.com

2
So we put the
equation into our
table.

1

2
3

4

singaporestudent.com

3
Highlight the part
of the equation
that contain
x2 and x only.

1

2
3

Do not highlight
the constant.

4

singaporestudent.com

4
Call this
expression as ‘p’.

1

2
3

4

singaporestudent.com

5
Rewrite 6x as
(2)(3) x.

1

2
3

4

singaporestudent.com

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

1

2
3
4

singaporestudent.com

7
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

singaporestudent.com

8
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

singaporestudent.com

a=x
b=3

9
1

Add 32 to p.

2

Call this
expression : q

3
4

singaporestudent.com

10
1

Add 32 to p.

2

Call this
expression : q

3
4

a b

2

a

2

2ab b

2

singaporestudent.com

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.
singaporestudent.com

12
a b

4

2

a2

2ab b 2

a=x
b=3

5

6

7

8

singaporestudent.com

13
a b
4

2

a2

2ab b 2

a=x
b=3

5

There! We applied
the formula.

6

7

8

singaporestudent.com

14
4

since

then

5

6

7

8

singaporestudent.com

15
4

since
5

then

6

7

8

singaporestudent.com

16
4

Simplify y.
5

-9 + 5 is 4

6

7

8

singaporestudent.com

17
Question :

Answer :

singaporestudent.com

18

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Completing the square v002