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Math Help - Quadratic Equation

  1. #1
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    Quadratic Equation

    Please, see attachment for quadratic equation. As a first step, do I rewrite sqrt{22x} as (22x)^(1/2)?

    Is this correct: x^2 + (22x)^(1/2) = 0

    See attachment.
    Attached Thumbnails Attached Thumbnails Quadratic Equation-quadratic-equation.jpg  
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  2. #2
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    Quote Originally Posted by sologuitar View Post
    Please, see attachment for quadratic equation. As a first step, do I rewrite sqrt{22x} as (22x)^(1/2)?

    Is this correct: x^2 + (22x)^(1/2) = 0

    See attachment.
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  3. #3
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    Quote Originally Posted by sologuitar View Post
    Please, see attachment for quadratic equation. As a first step, do I rewrite sqrt{22x} as (22x)^(1/2)?

    Is this correct: x^2 + (22x)^(1/2) = 0

    See attachment.
    If you like, it doesn't make a difference

    x^2 = -\sqrt{22x}

    Square both sides

    x^4 = 22x

    x^4-22x=0

    x(x^3-22)=0

    Either x=0 or x^3-22=0

    You can use the difference of two cubes to solve

    I get
    x=0

    x = \sqrt [3]{22}

    x=\frac{-\sqrt [3]{22}+i\,\sqrt{3\sqrt [3]{22^2}}}{2}

    x=\frac{-\sqrt [3]{22}-i\,\sqrt{3\sqrt [3]{22^2}}}{2}

    Some of these answers may not be correct, sub into the original equation to check. Also the last two answers are complex
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  4. #4
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    OK...

    Quote Originally Posted by e^(i*pi) View Post
    If you like, it doesn't make a difference

    x^2 = -\sqrt{22x}

    Square both sides

    x^4 = 22x

    x^4-22x=0

    x(x^3-22)=0

    Either x=0 or x^3-22=0

    You can use the difference of two cubes to solve

    I get
    x=0

    x = \sqrt [3]{22}

    x=\frac{-\sqrt [3]{22}+i\,\sqrt{3\sqrt [3]{22^2}}}{2}

    x=\frac{-\sqrt [3]{22}-i\,\sqrt{3\sqrt [3]{22^2}}}{2}

    Some of these answers may not be correct, sub into the original equation to check. Also the last two answers are complex
    I had never seen a quadratic equation like that before.
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  5. #5
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    Quote Originally Posted by sologuitar View Post
    I had never seen a quadratic equation like that before.
    Yeah, it comes from the difference of two cubes and because 22 is not a perfect cube, annoying isn't it? XD
    The good news is if you only want real values of x you can discard the bottom two solutions I gave
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