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# why do i need both positive and negative values (completing the square)

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1. (x+0.4)^2 = 4

(x+0.4) = ±2

x =1.6 or x = -2.4

i know that square rooting gives you negative and positive answer, but why, why ±??

another example is the quadratic equation where theres the ±
2. (Original post by ihatePE)

i know that square rooting gives you negative and positive answer, but why, why ±??
It doesn't. This is a common misconception.

http://www.thestudentroom.co.uk/show....php?t=3173187

All the best
3. +/- basically means the result is both positive and negative of the number. You can write the answer as separated positive and negatives (e.g. 2 and -2 instead of +/-2).

Above pretty much said what else is needed.
4. (Original post by ihatePE)
(x+0.4)^2 = 4

(x+0.4) = ±2

x =1.6 or x = -2.4

i know that square rooting gives you negative and positive answer, but why, why ±??

another example is the quadratic equation where theres the ±

-2^2 = 4 , 2^2 = 4

therefore if your answer is √4, it could be any of those two values unless they specify x>0, etc...

Its easier to notate it ±2, than writing out the former.
5. (Original post by ihatePE)
(x+0.4)^2 = 4
This is asking "what number(s) do I need to add 0.4 to and then square the whole thing to get 4?".

So we break it down into steps:

1) what number(s) do I need to square to get 4

2) what number do I need to add 0.4 and then square to get 4.

So the first step, there are two numbers that square to give 4, that is: +2 or -2. We write these as , it's saying "2 or -2" are solutions to the equation y^2 = 4.
6. (Original post by SeanFM)
It doesn't. This is a common misconception.

http://www.thestudentroom.co.uk/show....php?t=3173187

All the best

thanks! looking at these equations on graphs make my head dizzy but i'll get used to it.
7. You really didn't know that (-2)^2 and 2^2 = 4?

Posted from TSR Mobile
8. (Original post by Vikingninja)
+/- basically means the result is both positive and negative of the number. You can write the answer as separated positive and negatives (e.g. 2 and -2 instead of +/-2).

Above pretty much said what else is needed.
(Original post by 34908seikj)
-2^2 = 4 , 2^2 = 4

therefore if your answer is √4, it could be any of those two values unless they specify x>0, etc...

Its easier to notate it ±2, than writing out the former.
(Original post by Zacken)
This is asking "what number(s) do I need to add 0.4 to and then square the whole thing to get 4?".

So we break it down into steps:

1) what number(s) do I need to square to get 4

2) what number do I need to add 0.4 and then square to get 4.

So the first step, there are two numbers that square to give 4, that is: +2 or -2. We write these as , it's saying "2 or -2" are solutions to the equation y^2 = 4.
thank ou everyone, i just got one more question before i move on
the question is

2x^2 - x - 6 = 0

using the quadratic formula i got x = -2 and x= 1.5
when i factorised it i got x=2 and x=-1.5

the -b was 1 instead of -1? how?
9. (Original post by ihatePE)
thank ou everyone, i just got one more question before i move on
the question is

2x^2 - x - 6 = 0

using the quadratic formula i got x = -2 and x= 1.5
when i factorised it i got x=2 and x=-1.5

the -b was 1 instead of -1? how?
-b would be indeed 1 as it is -1(-1) = 1
10. (Original post by eternaforest)
You really didn't know that (-2)^2 and 2^2 = 4?

Posted from TSR Mobile
i know that, my question was worded awkwardly, i was just wondering if its ok to just write one value instead of two
11. (Original post by ihatePE)
thank ou everyone, i just got one more question before i move on
the question is

2x^2 - x - 6 = 0

using the quadratic formula i got x = -2 and x= 1.5
when i factorised it i got x=2 and x=-1.5

the -b was 1 instead of -1? how?
Because the coefficient of the x was -1 so b= -1 and so -b = 1.
12. (Original post by ihatePE)
2x^2 - x - 6 = 0

Look at your equation, that is:

2x^2 + (-1)x + (-6) = 0.

So a = 2, b =-1, c = -6.

So .
13. (Original post by 34908seikj)
-b would be indeed 1 as it is -1(-1) = 1
(Original post by Zacken)
Look at your equation, that is:

2x^2 + (-1)x + (-6) = 0.

So a = 2, b =-1, c = -6.

So .

ahhh, these little details can give me wrong answers which scares me from maths
14. (Original post by ihatePE)
i know that, my question was worded awkwardly, i was just wondering if its ok to just write one value instead of two
If it's a quadratic question then you'll probably always need to give the two answers but in general when you have rt4 you don't have to put +/-2

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15. Real fun starts when you solve equations like
16. (Original post by RDKGames)
Real fun starts when you solve equations like
I see what you did there
17. (Original post by Zacken)
Look at your equation, that is:

2x^2 + (-1)x + (-6) = 0.

So a = 2, b =-1, c = -6.

So .
(Original post by 34908seikj)
-b would be indeed 1 as it is -1(-1) = 1
(Original post by Vikingninja)
Because the coefficient of the x was -1 so b= -1 and so -b = 1.
(Original post by SeanFM)
I see what you did there
hai lovely maths peepo i have a question, im trying to complete the square of 3[(x-2)^2 - 4x + 17/3]but i dont understand whether you half 4 or -4?
18. (Original post by ihatePE)
hai lovely maths peepo i have a question, im trying to complete the square of 3[(x-2)^2 - 4x + 17/3]but i dont understand whether you half 4 or -4?
I would expand the whole (x-2)^2 out to get: then you'd be halving to get
19. (Original post by ihatePE)
hai lovely maths peepo i have a question, im trying to complete the square of 3[(x-2)^2 - 4x + 17/3]but i dont understand whether you half 4 or -4?
Neither. To me, it looks like you need to expand the brackets (x-2)^2 first.

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