# Completing the square

Presentation on Completing the square for GCSE Mathematics.

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• Created by: waqaar
• Created on: 14-05-08 14:47

## Other slides in this set

### Slide 2

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Another method for solving quadratic equations is
Completing The Square
You will remember that:
Which gives:
This is the basic principle behind completing the square…read more

### Slide 3

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Completing the square
Complete the square for x2 ­ 10x.
Compare this expression to (x ­ 5)2 = x2 ­ 10x + 25
x2 ­ 10x = x2 ­ 10x + 25 ­ 25
= (x ­ 5)2 ­ 25
Complete the square for x2 ­ 3x.
Compare this expression to (x ­ 1.5)2 = x2 ­ 3x + 2.25
x2 ­ 3x = x2 ­ 3x + 2.25 ­ 2.25
= (x - 1.5)2 ­ 2.25…read more

### Slide 4

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2
Expressions in the form x + bx…read more

### Slide 5

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Completing the square
How can we complete the square for
x2 + 8x + 9?
Look at the coefficient of x.
This is 8 so compare the expression to (x + 4)2 = x2 + 8x + 16.
x2 + 8x + 9 = x2 + 8x + 16 ­ 7
= (x + 4)2 ­ 7
In general,
x2 + 2ax + b = x + a 2 ­ a
2

### Slide 6

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Completing the square
Complete the square for x2 + 12x ­ 5.
Compare this expression to (x + 6)2 = x2 + 12x + 36
x2 + 12x ­ 5 = x2 + 12x + 36 ­ 41
= (x + 6) 2 ­ 41
Complete the square for x2 ­ 5x + 16
Compare this expression to (x ­ 2.5)2 = x2 ­ 5x + 6.25
x2 ­ 5x + 16 = x2 ­ 5x + 6.25 + 9.75
= (x2 ­ 2.5) + 9.75…read more