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4 February, 23:51

Finding the roots by completing the square

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  1. 4 February, 23:55
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    For y=x^2-6x-11

    complete the square

    so roots

    set y=0

    0=x^2-6x-11

    group x terms

    0 = (x^2-6x) - 11

    take 1/2 of linear coefient (-6) and square it

    -6/2=-3, (-3) ^2=9

    add positive and neative to inside of parenthasees

    0 = (x^2-6x+9-9) - 11

    complete square

    0 = ((x-3) ^2-9) - 11

    expand

    0 = (x-3) ^2-9-11

    0 = (x-3) ^2-20

    add 20 to both sides

    20 = (x-3) ^2

    sqrt both sides

    remember positive and negative roots

    +/-2√5=x-3

    add 3 to both sides

    3+/-2√5=x

    so

    x=3+2√5 and 3-2√5
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