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Math Help - Factoring

  1. #1
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    Factoring

    is it possible to factor this??

    20s^2-49st+30t^2

    the closest i can get is -30 times -20 but the sum of that equal -50
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  2. #2
    Eater of Worlds
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    Rewrite as:

    How about -24 and -25. -24-25=-49, (-24)(-25)=600

    20s^{2}-24st-25st+30t^{2}

    4s(5s-6t)-5t(5s-6t)

    (4s-5t)(5s-6t)
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  3. #3
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    Hello, t-dot!

    Is it possible to factor this: . 20s^2-49st+30t^2
    If you're desperate, you can use the Quadratic Formula.


    Consider the quadratic: . 20x^2 - 49x + 30 \:=\:0

    Quadratic Formula: . x \;=\;\frac{-(-49) \pm \sqrt{(-49)^2 - 4(20)(30)}}{2(20)} \;=\;\frac{49 \pm \sqrt{1}}{40}

    And we have: . x \;=\;\frac{49\pm1}{40} \;=\;\begin{array}{ccccc}\dfrac{49+1}{40} & = & \dfrac{50}{40} & = & \dfrac{5}{4} \\ \dfrac{49-1}{50} & = & \dfrac{48}{40} & = & \dfrac{6}{5}\end{array}


    Now we can run the problem backwards:

    . . x \:=\:\frac{5}{4}\quad\Rightarrow\quad 4x \:=\:5\quad\Rightarrow\quad 4x-5 \:=\:0

    . . x \:=\:\frac{6}{5}\quad\Rightarrow\quad 5x \:=\:6\quad\Rightarrow\quad 5x-6\:=\:0


    So the equation was: . (4x-5)(5x-6) \;=\;0

    . . and the quadratic is: . 20x^2 - 49x + 30 \;=\;0


    Therefore: . 20s^2 - 49st + 30t^2 \;=\;(4s-5t)(5s-6t)

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, t-dot!

    If you're desperate, you can use the Quadratic Formula.


    Consider the quadratic: . 20x^2 - 49x + 30 \:=\:0

    Quadratic Formula: . x \;=\;\frac{-(-49) \pm \sqrt{(-49)^2 - 4(20)(30)}}{2(20)} \;=\;\frac{49 \pm \sqrt{1}}{40}

    And we have: . x \;=\;\frac{49\pm1}{40} \;=\;\begin{array}{ccccc}\dfrac{49+1}{40} & = & \dfrac{50}{40} & = & \dfrac{5}{4} \\ \dfrac{49-1}{50} & = & \dfrac{48}{40} & = & \dfrac{6}{5}\end{array}


    Now we can run the problem backwards:

    . . x \:=\:\frac{5}{4}\quad\Rightarrow\quad 4x \:=\:5\quad\Rightarrow\quad 4x-5 \:=\:0

    . . x \:=\:\frac{6}{5}\quad\Rightarrow\quad 5x \:=\:6\quad\Rightarrow\quad 5x-6\:=\:0


    So the equation was: . (4x-5)(5x-6) \;=\;0

    . . and the quadratic is: . 20x^2 - 49x + 30 \;=\;0


    Therefore: . 20s^2 - 49st + 30t^2 \;=\;(4s-5t)(5s-6t)


    thanks but i'm not quite sure i understand this way of solving it.
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