I'm confused...........

This was in my content but I don't understand it...

f(x) = 2x² - 20x + 45
f(x) = 2(x² - 10x) + 45
= 2(x² - 10x + 25 - 25) + 45
= 2(x² - 10x + 25) - 50 + 45
= 2(x - 5)² - 5

Where does the 24 suddenly appear from?

Many thanks for any help! =)

it is called completing the square

When you have something like
x^2 +bx
and you want to convert it to something like
x^2 +bx +c
take half of the b term, square it, add it and subtract it or add it once to each side of an equation. NOTE: To do this, the coefficient on the x^2 term must be 1.

Example:

x^2 + 10x = 0
take 1/2 of the b term which is 10
so 1/2 of 10 = 5
then square it to get 25

x^2 + 10x + 25 = 25 (to keep the equation balanced)
then you can rewrite as follows

(x + 5)^2 = 25


In your example,
it was simply added it and subtracted it on the same side (essentially adding zero)

x^2 + 10x
x^2 + 10x + 25 - 25 (adding zero doesn't change the equation but allows manipulation)
(x + 5)^2 - 25

Jim

f(x) = 2x² - 20x + 45

f(x) = 0

x1 = 1/4(20 + 2 √(10)) = [10 + √(10)]/2

x2 = [10 - √(10)]/2

f(x) = 2 {x - [10 - √(10)]/2}*{x - [10 + √(10)]/2}

what are you trying to get in fact?

30 = 2· 15 = 2· 3· 5

There is an error in the solving