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k asked in Science & MathematicsMathematics · 2 months ago

What are the two answers to Sqrt 3x = x-6 ?

There should be two values of x, but only one of them solves the equation.

If possible, please show work so I can use the example for more of these problems 

3 Answers

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  • 2 months ago
    Favorite Answer

    √(3x) = x - 6

    (√(3x))² = (x - 6)²

    3x = x² - 12x + 36

    x² - 15x + 36 = 0

    (x - 3)(x - 12) = 0

    x - 3 = 0 or x - 12 = 0

    x = 3 or x = 12

    Check:

    When x = 3:

    L.H.S. = √(3*3) = 3

    R.H.S. = 3 - 6 = -3

    Since L.H.S. ≠ R.H.S., reject x = 3

    When x = 12:

    L.H.S. = √(3*12) = 6

    R.H.S. = 12 - 6 = 6

    L.H.S. = R.H.S., accept x = 3

    The answer: x = 12

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  • 2 months ago

    Same advice. Learn to use parentheses. see the solutions to what you meant. [Technically the left side reads "compute the sqrt  of 3 .. and then multiply that answer times the variable x." ] research PEDMAS

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  • 2 months ago

    √(3x) = (x - 6)

    3x = x^2 - 12x + 36

    x^2 - 15x + 36 = 0

    x^2 - 12x - 3x + 36 = 0

    x(x - 12) - 3(x - 12) = 0

    (x - 3)(x - 12) = 0

    Solutions:

    x = 3

    x = 12

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