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does completing the square and the quadratic formula give same results? Watch

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    i was doing some log questions and tried to complete the square of 6x^2 - 28x +16

    which gave me x=3 x=1.65 (must have done something super wrong)

    and then the quad formula gave me x=4 x=2/3 which is the right answer from markscheme.


    this is before i realised i could simplify it and simply factorise, but it made me think do they give different results or did i just do it incorrectly
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    The quadratic formula comes from completing the square on the quadratic  ax^2 + bx + c. They both give the same answer, because a quadratic always has the same set of solutions.
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    (Original post by ihatePE)
    i was doing some log questions and tried to complete the square of 6x^2 - 28x +16

    which gave me x=3 x=1.65 (must have done something super wrong)

    and then the quad formula gave me x=4 x=2/3 which is the right answer from markscheme.


    this is before i realised i could simplify it and simply factorise, but it made me think do they give different results or did i just do it incorrectly
    You just completed the square incorrectly.

    https://www.thestudentroom.co.uk/sho....php?t=4246394
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    The quadratic formula is just a generalised for of completing the square

    x^2 +(b/a)x +(c/a) = 0
    (x+(b/2a))^2 +(4ca-b^2)/(4a^2)=0
    x+(b/2a) = +-sqrt(b^2-4ac)/2a
    x=(b/2a) +-sqrt(b^2-4ac)/2a
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    I second what trythis has said above.

    In fact it is very simple to derive the quadratic formula from the general form of a quadratic equation by completing the square. See attachment (apologies for my messy handwriting)
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