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

It doesn't. This is a common misconception.

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

All the best

+/- 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.

-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.

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 $\pm 2$, it's saying "2 or -2" are solutions to the equation y^2 = 4.

You really didn't know that (-2)^2 and 2^2 = 4?

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-b would be indeed 1 as it is -1(-1) = 1

Look at your equation, that is:

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

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

So $-b = -(-1) =+ 1$.

Real fun starts when you solve equations like $x^2+2x+2=0$

Look at your equation, that is:

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

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

So $-b = -(-1) =+ 1$.

-b would be indeed 1 as it is -1(-1) = 1

Because the coefficient of the x was -1 so b= -1 and so -b = 1.

I see what you did there