Math

What is the answer to 12 squared = x(x+6) ?

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asked by Taylor
  1. 12 squared = x(x+6)

    144 = 2x +6x
    144 = 8x
    144/8 = 8x/8
    18 = x

  2. oh....it's false
    12 squared=x(x+6)
    144=x²+6x
    x²+6x+9=153
    (x+3)²=153

    answers: x+3=3*sqrt(17)
    or x+3=-3*sqrt(17)

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  3. OOPS, x(x+6) = x^2 + 6x

    so x^2 + 6x - 144 = 0

    x = (-3 ±√153)

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    posted by Reiny
  4. what do the question marks signify?

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    posted by Taylor
  5. Oops! is right. I goofed. Please disregard my answer.

  6. Hi:

    Given 12^2 = x(x+6), we have 144 = x^2 + 6x. Now, setting one side equal to zero gives x^2 + 6x - 144 = 0. The quadratic is not factorable (do you know why?) so we use the quadratic formula to get,

    x = 0.5[-6 +/- sqrt(36 - 4(-144))]

    = 0.5[-6 +/- sqrt(612)]

    = 0.5[-6 +/- 6sqrt(17)]

    = -3 +/- 3sqrt(17)

    = -3(1 +/- SQRT(17))

    So your two solutions are
    x = -3(1 + sqrt(17)) and
    x = -3(1 - sqrt(17)).

    Regards,

    Rich B.

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    posted by rich
  7. you're right but saying x²+6x-144=0 is not factorable, it is a mistake
    x²+6x-144=x²+6x+9-153=(x+3)²-153=(x+3+sqrt(153))*(x+3-sqrt(153))
    so u can factorize it

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  8. It is generally agreed in both the US and Canada that "factoring" is restricted to the set of rational numbers.

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    posted by Reiny
  9. ok, thanks.
    in france 'factoring'is restricted to 3 'identities' as a²-b²=(a-b)(a+b)
    a²+2ab+b²=(a+b)² and a²-2ab+b²=(a-b)²...so diferents countries=diferents matematics lol

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  10. That makes very little sense.

    You mean 10x^2 + 13x - 3 = (2x+3)(5x-1)
    would not be acceptable in France??
    I doubt that very much.

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    posted by Reiny
  11. sorry, but u say that 'factoring' is restricted to the set of rational numbers..and about the cumplex numbers???

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  12. mk-tintin:

    Yes, of course. However, as another member writes, I assume one understands my meaning specifically as irreducible over the rationals, Q.

    Rich B.

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    posted by rich

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