can someone please explain why it is a -4 even tho we are completing square. I understand half of -4=-2 but -2^2 is 4, not -4
#Completing the square?
inner sluice
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can someone please explain why it is a -4 even tho we are completing square. I u...
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rancid ibex
can someone please explain why it is a -4 even tho we are completing square. I u...
6(x^2 - 4x) + 25
= 6(x^2 - 4x + 4 - 4) + 25
= 6((x - 2)^2 - 4) + 25```
haughty bane
the expansion of (x-2)^2 is x^2 -4x + 4. Because we cant randomly add 4 to the equation we neutralize it by adding a -4 to make it equal the same equation as before while completing it into a square
inner sluice
```
6(x^2 - 4x) + 25
= 6(x^2 - 4x + 4 - 4) + 25
= 6((x - 2)^2 - 4) + 25```
i’m sorry, i understood none of that
haughty bane
wait let me explain
rancid ibex
i’m sorry, i understood none of that
...we add and subtract 4.
Which is equivalent to adding 0.
Then the positive 4 goes into the square, and the negative 4 stays out.
haughty bane
the expansion of (x-2)^2 is x^2 -4x + 4. Because we cant randomly add 4 to the e...
i may be suck at explaining tbh dont mind me.
rancid ibex
when u add the -4 to neutralise
...no.
haughty bane
no in fact if we dont add it it unbalances the equation
rancid ibex
6(x^2 - 4x) + 25
= 6(x^2 - 4x + 4 - 4) + 25```Do you agree with this @inner sluice?yes
rancid ibex
So then do you agree with this: 6(x^2 - 4x + 4 - 4) + 25 = 6((x^2 - 4x + 4) - 4) + 25?
inner sluice
yea, it’s just brackets
haughty bane
factorize it
rancid ibex
And x^2 - 4x + 4 = (x - 2)^2, so that means: 6((x^2 - 4x + 4) - 4) + 25 = 6((x - 2)^2 - 4) + 25
inner sluice
ohhh
haughty bane
no okay read what techie literate texts i dont wanna confuse u
rancid ibex
it makes sense
Glad to help.
inner sluice
so u can just add brackets wherever you want
rancid ibex
Not always.
inner sluice
so why was that the case bere
rancid ibex
We used the commutative property of addition to do that.
Er, I mean the associative property.
The associative property of addition.
inner sluice
ok
rancid ibex
Addition and multiplication are assosiative, but not all other operations are.
inner sluice
thank you both, @haughty bane @rancid ibex
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@inner sluice has given 1 rep to @haughty bane @rancid ibex
inner sluice
Addition and multiplication are assosiative, but not all other operations are.
seems like a lot of effort
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