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    Hey guys,
    Im very frustrated I cannot see a method to answer this question correctly.
    Any help is much appreciated.

    'Two rectangles have the same are but different dimensions. The dimensions of the first are (2x + 2) by (x - 1) and the second are (x + 3) by (x + 1).
    Find value of x and the area.'

    I (think I) know what x equals but only by expanding and substituting until I found a number that satisfied the equality. ie. 2x^2 - 2 = x^2 - 4x + 3
    (x = 5, area = 48). I know that this is not the way to go about it. Can anyone help with the correct method? I tried to differentiate but that didnt seem to get me anywhere.
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    Do you not know how to solve a quadratic equation? ._.
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    Your equality is incorrect it should say

    (Original post by jdinsaanen)
    2x^2 - 2 = x^2 + 4x + 3
    From here you get x^2 - 4x - 5

    And that gives (x+1)(x-5)

    Since x is not -1 it must be 5
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    (Original post by jdinsaanen)
    Hey guys,
    Im very frustrated I cannot see a method to answer this question correctly.
    Any help is much appreciated.

    'Two rectangles have the same are but different dimensions. The dimensions of the first are (2x + 2) by (x - 1) and the second are (x + 3) by (x + 1).
    Find value of x and the area.'

    I (think I) know what x equals but only by expanding and substituting until I found a number that satisfied the equality. ie. 2x^2 - 2 = x^2 - 4x + 3
    (x = 5, area = 48). I know that this is not the way to go about it. Can anyone help with the correct method? I tried to differentiate but that didnt seem to get me anywhere.
    Recap

    Given

    ax^2 + bx + c =0

    x=\dfrac{-b \pm \sqrt{b^2 - 4ac }}{2a}

    as long as

    b^2 \geq 4ac

    (if this is not true, then the roots aren't real, i.e they are complex).

    However, in this case, you have sufficiently nice values of a and b to factorise the equation into the form

    (x-m)(x-n)=0

    where m and n are such that

    am^2 + bm + c =0

    an^2 + bn + c=0

    In order to do this, you look for two numbers (here, they are m and n) such that their sum is b and their product is c.

    You are ONLY after the positive solution as lengths cannot be negative.
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    (Original post by TenOfThem)
    From here you get x^2 - 4x - 5

    And that gives (x+1)(x-5)

    Since x is not -1 it must be 5
    Sorry, I just dont see how you got x^2 - 4x - 5

    The rest I understand.
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    (Original post by Indeterminate)
    Recap
    Thank you for your feedback. I understand the uses of the discriminant but Im not getting answers for x that make any sense when I use the quadratic formula.
    I know I missing something obvious but it just not coming to me.
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    (Original post by jdinsaanen)
    Thank you for your feedback. I understand the uses of the discriminant but Im not getting answers for x that make any sense when I use the quadratic formula.
    I know I missing something obvious but it just not coming to me.
    Subtract

    (x^2 + 4x + 3)

    from both sides of the equation.
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    (Original post by Indeterminate)
    Subtract

    (x^2 + 4x + 3)

    from both sides of the equation.
    Many thanks for your help. Ive got it.
 
 
 
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