1. How to solve a quadratic in your head
Paul Carson
How to solve a quadratic in your head

2. About the talk 5 min talk Maths tutor of 16 years experience
Invented own method of learning and doing maths
Revolutionary methods compared to school
One example – solving a quadratic.

3. scope Squaring numbers Completing the square – how and its meaning
Solving the quadratic
example.

4. Squaring numbers
We need to be able to square numbers to complete the square
How to square numbers that end in 5
25 2 = 625
Take our leading number (2) and multiply by its next (3). Hook on 25.

5. Completing the square f(𝑥) = 𝑥 2 +3𝑥+ 2 ( 𝑥+1.5) 2 – 0.25
( 𝑥+1.5) 2 – 0.25
This represents the co-ordinate of the minimum, (-1.5, -0.25)

6. Solving the quadratic www.paulcarsonmaths.co.uk F(𝑥) = 𝑥 2 +3𝑥+ 2 = 0
( 𝑥+1.5) 2 – 0.25 = 0
Rearrange for 𝑥: gives
𝑥=−1.5±√0.25
Always perform this – skip to the end!
Solutions are always min value +- sq root of y value

7. example F(x) = 𝑥 2 +7𝑥+ 1 ( 𝑥+3.5) 2 – 11.25 Solutions; yes –
( 𝑥+3.5) 2 – 11.25
Solutions; yes –
𝑥=−3.5±√11.25

8. More available here Amazon E-book for kindle, iphone, laptop, etc.

9. Please come and talk to me with any questions
Thank you
Please come and talk to me with any questions