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

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    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
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    (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: (a+b)(a-b) = a^2 - b^2. In this case, you have 2^2 - x^2 , so what does that factorise as? hint: a=2, b=x.
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    (Original post by Zacken)
    You should know the difference of squares: (a+b)(a-b) = a^2 - b^2. In this case, you have 2^2 - x^2 , so what does that factorise as? hint: a=2, b=x.
    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
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    (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?
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    (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!
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    (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.
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    (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 ab= 0 then a = 0 or b=0.
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    (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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