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    my mind's gone blank and i can't seem to solve this basic equation through factorising- anyone know what i need to do?

    3x2 + 5x = 0
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    There is an x common in both terms.
    So we can say 3x^2+5x=x(3x+5).
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    (Original post by entertainmyfaith)
    my mind's gone blank and i can't seem to solve this basic equation through factorising- anyone know what i need to do?

    3x2 + 5x = 0
    common factor of x

    factorise -> x(3x + 5) = 0

    so x = 0 or x = -5/3
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    (Original post by DrDyk)
    common factor of x

    factorise -> x(3x + 5) = 0

    so x = 0 or x = -5/3
    i'm sorry how did you get -5/3? it's not wrong because i've checked the textbook answer i just can't work out how you got it
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    (Original post by entertainmyfaith)
    i'm sorry how did you get -5/3? it's not wrong because i've checked the textbook answer i just can't work out how you got it
    So in order to get ' (x)(3x + 5) ' equal to 0, one of the brackets (you can imagine brackets around the x on its own) has to be equal to zero. Anything multiplied by 0 is 0.

    so, if x = 0, the first bracket is 0 and the whole equation must equal 0.

    if x = -5/3, the second bracket is 0 and so the whole equation must equal 0.

    You can work out the second bracket by putting 3x+ 5 = 0

    3x+5 = 0 -> 3x = -5 -> x = -5/3

    Hope this helps
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    When you have the following equation:



    For this to be true, either x = 0 or the inside of the brackets must equal zero, as something multiplied by zero equals zero.

    So now ask, "what does x need to be for the inside of the brackets to equal zero?", we can do that trivially by rearranging the equation:

    3x + 5 = 0
    3x = -5
    x =(-5/3)

    This makes sense, as multiplying -5/3 by three gives -5, and -5 + 5 equals zero.
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    (Original post by entertainmyfaith)
    i'm sorry how did you get -5/3? it's not wrong because i've checked the textbook answer i just can't work out how you got it
    If x(3x+5) = 0 then either x=0 or 3x+5 = 0. You can solve the latter to get your second solution Does this make sense?
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    (Original post by DrDyk)
    So in order to get ' (x)(3x + 5) ' equal to 0, one of the brackets (you can imagine brackets around the x on its own) has to be equal to zero. Anything multiplied by 0 is 0.

    so, if x = 0, the first bracket is 0 and the whole equation must equal 0.

    if x = -5/3, the second bracket is 0 and so the whole equation must equal 0.

    You can work out the second bracket by putting 3x+ 5 = 0

    3x+5 = 0 -> 3x = -5 -> x = -5/3

    Hope this helps
    ah that makes sense thank you!
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    (Original post by entertainmyfaith)
    ah that makes sense thank you!
    Graph of 3x2 + 5x = 0

    Name:  graph.PNG
Views: 28
Size:  44.4 KB

    Hopefully you can see, when x = 0 and x = -5/3, the y value of the corresponding graph is 0. This is why there are two solutions for when this equation equals 0.
 
 
 
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