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    I am trying to solve this simultaneous equation but I can't factorise it so either I am going wrong in the equation or I am missing out something while trying to factorise.

    Anyway help will be appreciated.

    3x^2 + y^2 = 28

    3x + y = 8 (Linear)

    8 - 3x = y

    3x^2 + (8 - 3x)^2 = 28


    3x^2 + 64 - 48x + 9x^2 = 28

    12x^2 - 48x + 36 = 0
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    64 - 28 = 36.
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    (Original post by Glutamic Acid)
    64 - 28 = 36.
    My bad I meant to type 36 I still can't factorise the f*king thing should I be able to factorise that?
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    It does factorise, try dividing through by 12 and see if that makes it any clearer.
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    Thanks, got sorted now, it was a moment of not being able to see the wood for the tree's.
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    Hit another problem on simultaneous question:
    Is this working out correct?
    2x + y = 8 Y=2x - 8
    4x^2 + 3y^2 = 52

    4x^2 + 3(2x - 8)^2 = 52

    4x^2 + 3(4x^2 - 32x + 64) = 52

    4x^2 + 12x^2 - 96x + 192 = 52

    16x^2 - 96x + 140 = 0
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    Assuming the first line should be 2x + y = 8 and rearrangement, the rearrangement should actually be y = 8 - 2x

    Edit: Having said that, when substituted in, it squares to the same solution, so your final answer is, as far as I can see, correct.
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    (Original post by Shakaa)
    Hit another problem on simultaneous question:
    Is this working out correct?
    2x + y = 8 Y=2x - 8
    4x^2 + 3y^2 = 52

    4x^2 + 3(2x - 8)^2 = 52

    4x^2 + 3(4x^2 - 32x + 64) = 52

    4x^2 + 12x^2 - 96x + 192 = 52

    16x^2 - 96x + 140 = 0
    Method is fine, but you've got the first line wrong. Just complete the square and back substitute and you're done.
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    I realise this is often frowned upon in these forums, but can someone show me the steps in order to factorise/complete the square of the following in order the reach the answer? Its really doing my head in :/

    2x + y = 8 Y=2x - 8
    4x^2 + 3y^2 = 52

    4x^2 + 3(2x - 8)^2 = 52

    4x^2 + 3(4x^2 - 32x + 64) = 52

    4x^2 + 12x^2 - 96x + 192 = 52

    16x^2 - 96x + 140 = 0
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    (Original post by Shakaa)
    16x^2 - 96x + 140 = 0
    Last post for the day; and on this occasion only:

    Divide through by 16:

    x^2-6x + 35/4=0

    Complete the square:

    (x-3)^2 -9 +35/4 = 0

    (x-3)^2 = 1/4

    and I'm sure you can finish that.
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    (Original post by ghostwalker)
    Last post for the day; and on this occasion only:

    Divide through by 16:

    x^2-6x + 35/4=0

    Complete the square:

    (x-3)^2 -9 +35/4 = 0

    (x-3)^2 = 1/4

    and I'm sure you can finish that.
    I can't figure out why -9 +35/4 transforms into 1/4 :confused:
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    (Original post by Shakaa)
    I can't figure out why -9 +35/4 transforms into 1/4 :confused:
    (X-3)^2 -9 + 35/4 = 0 --> (X-3)^2 = 9 - 35/4

    convert 9 to it's fractional equivalent ( 9 = 9/1)
    so 9 = 36/4

    substituting in

    (X-3)^2 = 36/4 - 35/4

    leaving

    (X-3)^2 = 1/4

    Hope that makes it more clear
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    (Original post by GingerGoat)
    (X-3)^2 -9 + 35/4 = 0 --> (X-3)^2 = 9 - 35/4

    convert 9 to it's fractional equivalent ( 9 = 9/1)
    so 9 = 36/4

    substituting in

    (X-3)^2 = 36/4 - 35/4

    leaving

    (X-3)^2 = 1/4

    Hope that makes it more clear

    I don't full understand how it works but I understand what's happened now thanks.
 
 
 
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