1. Slideshow 16, Mathematics Mr Richard Sasaki, Room 307

2.  Objectives

3.  Solving through factorisation Example

4.  Completing the Square

5.  Example Completing the Square It makes it easier if we move the constant to the other side. We need ( x + 3) 2 = a. (Note 3 is half of 6 as this would produce 3x + 3x. To get ( x + 3) 2 we half 6 and then square it. 3 9 Now write the left as ( x + a) 2. Square root both sides and solve!

6.  Completing the Square There is a lot to remember! Example Halve and square. 16 = 2 or -10 You must show your working!

7.  Completing the Square

8.  When completing the square it is easy to make a small mistake, be careful! When we have a negative coefficient of x, the symbol within the squared brackets will also be negative. Make sure you carry the negative symbol!

9.  Negative Cases Example The addition to each side is always positive as (½ x ) 2 > 0.

10.  Completing the Square