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    Hi, quick help with a question: Express 4x^2-4x-3 in the form (ax-b)^2-c, where a, b and c are positive constants to be found.
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    (Original post by jamiee207)
    Hi, quick help with a question: Express 4x^2-4x-3 in the form (ax-b)^2-c, where a, b and c are positive constants to be found.
    What have you tried
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    I haven't really, I have no idea why I can't do it either, it's supposed to be trivial considering it's the first part on an early question in my homework.
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    (Original post by jamiee207)
    Hi, quick help with a question: Express 4x^2-4x-3 in the form (ax-b)^2-c, where a, b and c are positive constants to be found.
    What did you try?

    As a hint,

    4x^2-4x-3 = 4[x^2-x-3/4]
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    (Original post by jamiee207)
    I haven't really, I have no idea why I can't do it either, it's supposed to be trivial considering it's the first part on an early question in my homework.
    Well, what is your usual approach to questions on completing the square?
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    You need to complete the square.

    Firstly, consider the 4x^2. What multiplied by itself gives you 4x^2? This answer will be the ax part of your answer.

    Now, you need to consider the -4x. What number multiplied with your ax and added together gives you -4x? This will give you the -b part to your answer.

    Finally using your (ax-b)^2 break the bracket and see what you need to add or take away to make -3. This will give your-c part.

    It is a more complex version of completing the square.
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    (Original post by MathsGeek89)
    You need to complete the square.

    Firstly, consider the 4x^2. What multiplied by itself gives you 4x^2? This answer will be the ax part of your answer.

    Now, you need to consider the -4x. What number multiplied with your ax and added together gives you -4x? This will give you the -b part to your answer.

    Finally using your (ax-b)^2 break the bracket and see what you need to add or take away to make -3. This will give your-c part.

    It is a more complex version of completing the square.
    It's easier to factorise the 4 and then just do the usual completing the square technique on x^2 - x - 3/4. Then just multiply through by 4.
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    IMPORTANT NOTE : I am not sure of this answer
    a=4 b=-4 c=-3

    x= -b/2a
    = 4/8 = 0.5
    y = 4(0.5)^2-4(0.5)-3
    = -4
    change the sign of x
    4{(x-0.5)^2-4}
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    (Original post by Mohamed Mehaya)
    IMPORTANT NOTE : I am not sure of this answer
    a=4 b=-4 c=-3

    x= -b/2a
    = 4/8 = 0.5
    y = 4(0.5)^2-4(0.5)-3
    = -4
    change the sign of x
    4{(x-0.5)^2-4}
    There's no point learning maths if you're going to memorise silly rules/formulas to solve equations, that's not what maths is about. UNDERSTAND why completing the square works, don't memorise a formula to complete the square.
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    (Original post by Mohamed Mehaya)
    IMPORTANT NOTE : I am not sure of this answer
    a=4 b=-4 c=-3

    x= -b/2a
    = 4/8 = 0.5
    y = 4(0.5)^2-4(0.5)-3
    = -4
    change the sign of x
    4{(x-0.5)^2-4}
    Nearly, -4 isn't multiplied by 4 though.

    expanding

    4(x-0.5)^{2}-4 = 4(x^{2}-x+0.25)-4=4x^{2}-4x+1-4=4x^{2}-4x-3
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    (Original post by Swayum)
    There's no point learning maths if you're going to memorise silly rules/formulas to solve equations, that's not what maths is about. UNDERSTAND why completing the square works, don't memorise a formula to complete the square.
    There's a silly formula for completing the square?
 
 
 
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