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# Find the roots of: 4-x^2=0, how do I rearrange that to make it easier to factorise?

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1. I can find the root of something in the standard format like x^2 + 3x = 0 by factorising it to get (x+1)(x+2)=0, and then getting the roots that way, giving the answers of x= -1 and x= -2.

How can I rearrange: 4 - x^2 = 0 into that format so that I can factorise it in the same way as I did before in order to find the roots?
Can you walk me through the steps of rearranging and solving this one please?

Thanks
2. (Original post by blobbybill)
I can find the root of something in the standard format like x^2 + 3x = 0 by factorising it to get (x+1)(x+2)=0, and then getting the roots that way, giving the answers of x= -1 and x= -2.

How can I rearrange: 4 - x^2 = 0 into that format so that I can factorise it in the same way as I did before in order to find the roots?
Can you walk me through the steps of rearranging and solving this one please?

Thanks
You should know the difference of squares: . In this case, you have , so what does that factorise as? hint: .
3. (Original post by Zacken)
You should know the difference of squares: . In this case, you have , so what does that factorise as? hint: .
It factorises as (a+b)(a-b), so (2+x)(2-x)=0? But I don't have a value for x in this question, so i don't know how I would go about factorising it and then solving the roots.

I think, that it is like this: (2+x)(2-x)=0, so either (2+x)=0 or (2-x). If that is right, I don't know how you would proceed onwards from this point. Thanks
4. (Original post by blobbybill)
It factorises as (a+b)(a-b), so (2+x)(2-x)=0? But I don't have a value for x in this question, so i don't know how I would go about factorising it and then solving the roots.

I think, that it is like this: (2+x)(2-x)=0, so either (2+x)=0 or (2-x). If that is right, I don't know how you would proceed onwards from this point. Thanks
If x+2=0, what does x equal?
If x-2=0, what does x equal?
5. (Original post by B_9710)
If x+2=0, what does x equal?
If x-2=0, what does x equal?
x+2=0, so x=-2
x-2=0, so x=+2

So, the roots (and solutions) are either x=+2 or x=-2?

Thanks so much!
6. (Original post by blobbybill)
x+2=0, so x=-2
x-2=0, so x=+2

So, the roots (and solutions) are either x=+2 or x=-2?

Thanks so much!
Yes that's correct.
7. (Original post by blobbybill)
x+2=0, so x=-2
x-2=0, so x=+2

So, the roots (and solutions) are either x=+2 or x=-2?

Thanks so much!
Yep. This follows from the property of the reals that if then or .
8. (Original post by blobbybill)
x+2=0, so x=-2
x-2=0, so x=+2

So, the roots (and solutions) are either x=+2 or x=-2?

Thanks so much!
If you are unfamiliar with the difference of two squares, you could just rearrange to find x.

4 - x² = 0
add x² to both sides to get
x² = 4
and then square root making sure you include both the positive and negative solution.

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