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Math Help - Solve for X(2)

  1. #1
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    Solve for X(2)

    0=-\frac{\sqrt{x+2}(x-7)}{2}+12
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  2. #2
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    Quote Originally Posted by Punch View Post
    0=-\frac{\sqrt{x+2}(x-7)}{2}+12
    The method here is the same as before. If we multiply by 2 throughout:

    Again x > -2

    0 = -(x-7)\sqrt{x+2} + 24

    (x-7)\sqrt{x+2} = 24

    square both sides

    (x-7)^2(\sqrt{x+2})^2 = 24^2

    Simplify and solve for x. Remember to check for extraneous solutions
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  3. #3
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    I did it like this, however won't we get a power of 3 when we expand?
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Punch View Post
    I did it like this, however won't we get a power of 3 when we expand?
    Yep

    (x-7)^2(x+2)

    (x+2)(x^2-14x+49) = x^3-14x^2+49x+2x^2-28x+98

    Collect like terms: x^3-12x^2+21x+98

    x^3-12x^2+21x-478=0

    Solve for x, very tricky: http://www.wolframalpha.com/input/?i=x^3-12x^2%2B21x-478%3D0
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  5. #5
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    For general solution of the cubic, you might Google "Cardano". The history is interesting also.
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  6. #6
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    Quote Originally Posted by e^(i*pi) View Post
    The method here is the same as before. If we multiply by 2 throughout:

    Again x > -2

    0 = -(x-7)\sqrt{x+2} + 24

    (x-7)\sqrt{x+2} = 24

    square both sides

    (x-7)^2(\sqrt{x+2})^2 = 24^2

    Simplify and solve for x. Remember to check for extraneous solutions
    Just a correction.
    here x \geq -2
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