1. What happens when the quadratic is not equal to 0?
Now Solve these equations as usual 
By factorising first!
We must make the quadratic equal to 0!
Try get these into the general quadratic form 𝑥 2 +𝑏𝑥+𝑐=0
𝑥 2 −𝑥=30
𝑥 2 =2𝑥+8
10 = 7𝑥 − 𝑥 2
𝑥 𝑥+1 =12
𝑥+2 𝑥+3 =56
𝒙 𝟐 −𝒙−𝟑𝟎=𝟎
𝒙 𝟐 −𝟐𝒙−𝟖=𝟎
𝒙 𝟐 −𝟕𝒙+𝟏𝟎=𝟎
𝒙 𝟐 +𝒙−𝟏𝟐=𝟎
𝒙 𝟐 +𝟓𝒙−𝟓𝟎=𝟎

2. What have we done so far? Factorising Expressions
By common factor (what’s common, what’s left)
Into two brackets (which two numbers give me…)
Special cases (re-arrange, difference of two squares, take out common number)
Solving Equations BY FACTORISING
Into two brackets
By common factor
When the equation is NOT equal to 0

3. Solving Quadratics thought process
The highest power of 𝒙 is 2, then it is a quadratic, we need to solve this quadratic, we need to end up with 𝒙=𝒔𝒐𝒎𝒆𝒕𝒉𝒊𝒏𝒈 𝒐𝒓 𝒙=𝒔𝒐𝒎𝒆𝒕𝒉𝒊𝒏𝒈 𝒆𝒍𝒔𝒆
Is the quadratic equal to 0?
YES NO
Factorise Left Hand Side
Rearrange it to make it equal to 0
Equate both parts to 0
Move terms to LHS
Expand the LHS
Solve each equation

4. Factorise the Left Hand Side
The LHS can be
Already Factorised
(and = 0)
Needs to be Factorised
Two Terms?
Three terms?
The general quadratic
(𝒙 )(𝒙 )
Difference of two squares
By common factor
(𝒙 )(𝒙 − )
𝒙 (𝒙 − )

5. Solving Quadratics thought process
The highest power of 𝒙 is 2, then it is a quadratic, we need to solve this quadratic, we need to end up with 𝒙=𝒔𝒐𝒎𝒆𝒕𝒉𝒊𝒏𝒈 𝒐𝒓 𝒙=𝒔𝒐𝒎𝒆𝒕𝒉𝒊𝒏𝒈 𝒆𝒍𝒔𝒆
Is the quadratic equal to 0?
YES NO
Factorise Left Hand Side
Rearrange it to make it equal to 0
Equate both parts to 0
Solve each equation

6. Self-Assessment Work Take out your copybook
I will present a question on solving equations
Take some time to identify what needs to be done (don’t do anything)
Discuss your thoughts with a partner
We will identify what we need to do together
You will be given time to do it
Assess yourself:
I would have been able to identify what to do without help
Once I identified what to do, I could do it with no problems
I need to work on identifying what to do and how to do it

7. Solve 𝒙 𝒙+𝟖 =𝟎 Equation already equal to 0 LHS already factorised
Equate both parts to 0
Solve
𝒙=𝟎 𝒐𝒓 𝒙+𝟖=𝟎
𝒙=𝟎 𝒐𝒓 𝒙=−𝟖

8. Solve 𝑥+4 𝑥+9 =0 Equation already equal to 0 LHS already factorised
Equate both parts to 0
Solve
𝒙+𝟒=𝟎 𝒐𝒓 𝒙+𝟗=𝟎
𝒙=−𝟒 𝒐𝒓 𝒙=−𝟗

9. Solve 𝑥 2 +5𝑥=0 Equation already equal to 0
Need to factorise LHS by common factor
Equate both parts to 0
Solve
𝒙 𝒙+𝟓 =𝟎
𝒙=𝟎 𝒐𝒓 𝒙+𝟓=𝟎
𝒙=𝟎 𝒐𝒓 𝒙=−𝟓

10. Solve 2𝑥 2 −4𝑥=0 Equation already equal to 0
Need to factorise LHS by common factor
Equate both parts to 0
Solve
𝟐𝒙 𝒙−𝟐 =𝟎
𝟐𝒙=𝟎 𝒐𝒓 𝒙−𝟐=𝟎
𝒙=𝟎 𝒐𝒓 𝒙=𝟐

11. Solve 𝑥 2 +11𝑥+18=0 Equation already equal to 0
Need to factorise LHS bracket to bracket
Equate both parts to 0
Solve
(𝒙+𝟗)(𝒙+𝟐)=𝟎
𝒙=−𝟗 𝒐𝒓 𝒙=−𝟐

12. Solve 𝑥 2 −16𝑥+64=0 (𝒙−𝟖)(𝒙−𝟖)=𝟎 𝒙=𝟖 Equation already equal to 0
Need to factorise LHS bracket to bracket
Equate both parts to 0
Solve
(𝒙−𝟖)(𝒙−𝟖)=𝟎
𝒙=𝟖
Only one solution!

13. Solve 𝑥 2 −81=0 (𝒙−𝟗)(𝒙+𝟗)=𝟎 𝒙−𝟗=𝟎 𝒐𝒓 𝒙+𝟗=𝟎 𝒙=𝟗 𝒐𝒓 𝒙=−𝟗
Equation already equal to 0
Factorise a difference of two squares
Equate both parts to 0
Solve
(𝒙−𝟗)(𝒙+𝟗)=𝟎
𝒙−𝟗=𝟎 𝒐𝒓 𝒙+𝟗=𝟎
𝒙=𝟗 𝒐𝒓 𝒙=−𝟗

14. Solve 4𝑥 2 −25=0 (𝟐𝒙−𝟓)(𝟐𝒙+𝟓)=𝟎 𝟐𝒙−𝟓=𝟎 𝒐𝒓 𝟐𝒙+𝟓=𝟎 𝒙= 𝟓 𝟐 𝒐𝒓 𝒙= −𝟓 𝟐
Equation already equal to 0
Factorise a difference of two squares
Equate both parts to 0
Solve
(𝟐𝒙−𝟓)(𝟐𝒙+𝟓)=𝟎
𝟐𝒙−𝟓=𝟎 𝒐𝒓 𝟐𝒙+𝟓=𝟎
𝒙= 𝟓 𝟐 𝒐𝒓 𝒙= −𝟓 𝟐

15. Solve 𝑥 2 −6𝑥=16 𝑥 2 −6𝑥−16=0 𝒙−𝟖 𝒙+𝟐 =𝟎 𝒙−𝟖=𝟎 𝒐𝒓 𝒙+𝟐=𝟎 𝒙=𝟖 𝒐𝒓 𝒙=−𝟐
Equation not equal to 0
Move one term to the LHS
Factorise into two brackets
Equate both parts to 0
Solve
𝑥 2 −6𝑥−16=0
𝒙−𝟖 𝒙+𝟐 =𝟎
𝒙−𝟖=𝟎 𝒐𝒓 𝒙+𝟐=𝟎
𝒙=𝟖 𝒐𝒓 𝒙=−𝟐

16. Solve 3𝑥=28− 𝑥 2 𝑥 2 +3𝑥−28=0 𝒙+𝟕 𝒙−𝟒 =𝟎 𝒙+𝟕=𝟎 𝒐𝒓 𝒙−𝟒=𝟎 𝒙=−𝟕 𝒐𝒓 𝒙=𝟒
Equation not equal to 0
Move two terms to the LHS
Factorise into two brackets
Equate both parts to 0
Solve
𝑥 2 +3𝑥−28=0
𝒙+𝟕 𝒙−𝟒 =𝟎
𝒙+𝟕=𝟎 𝒐𝒓 𝒙−𝟒=𝟎
𝒙=−𝟕 𝒐𝒓 𝒙=𝟒

17. Solve 𝑥 𝑥−5 =24 𝒙 𝟐 −𝟓𝒙=𝟐𝟒 𝒙 𝟐 −𝟓𝒙−𝟐𝟒=𝟎 𝒙−𝟖 𝒙+𝟑 =𝟎 𝒙−𝟖=𝟎 𝒐𝒓 𝒙+𝟑=𝟎
Equation not equal to 0
Expand LHS first
Move one term to the LHS
Factorise into two brackets
Equate both parts to 0
Solve
𝒙 𝟐 −𝟓𝒙=𝟐𝟒
𝒙 𝟐 −𝟓𝒙−𝟐𝟒=𝟎
𝒙−𝟖 𝒙+𝟑 =𝟎
𝒙−𝟖=𝟎 𝒐𝒓 𝒙+𝟑=𝟎
𝒙=𝟖 𝒐𝒓 𝒙=−𝟑

18. Solve 𝑥+8 𝑥−2 =39 𝒙 𝟐 +𝟖𝒙−𝟐𝒙−𝟏𝟔=𝟑𝟗 𝒙 𝟐 −𝟔𝒙−𝟏𝟔−𝟑𝟗=𝟎 𝒙 𝟐 −𝟔𝒙−𝟓𝟓=𝟎
Equation not equal to 0
Expand LHS first
Move one term to the LHS
Factorise into two brackets
Equate both parts to 0
Solve
𝒙 𝟐 +𝟖𝒙−𝟐𝒙−𝟏𝟔=𝟑𝟗
𝒙 𝟐 −𝟔𝒙−𝟏𝟔−𝟑𝟗=𝟎
𝒙 𝟐 −𝟔𝒙−𝟓𝟓=𝟎
𝒙−𝟏𝟏 𝒙+𝟓 =𝟎
𝒙−𝟏𝟏=𝟎 𝒐𝒓 𝒙+𝟓=𝟎
𝒙=𝟏𝟏 𝒐𝒓 𝒙=−𝟓

19. Homework: Mixed Exercise
STP 9 Pg 229 Exercise 11g
1, 2, 3,11,12,19,20
If you have some time, review the pages before and you will see all the types – you have an example in the yellow box then questions to try underneath