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Math Help - Isolating a variable with a square root

  1. #1
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    Isolating a variable with a square root

    Having some trouble with this problem. I feel like I'm doing it incorrectly. Can someone show me how to do this step by step?
    for
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  2. #2
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    Re: Isolating a variable with a square root

    Quote Originally Posted by DasRabbit View Post
    Having some trouble with this problem. I feel like I'm doing it incorrectly. Can someone show me how to do this step by step?
    for
    \begin{align*}  -3\sqrt{x+4} &= -3 \\ \sqrt{x+4} &= 1  \\x+4 &= 1   \end{align*}
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  3. #3
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    Re: Isolating a variable with a square root

    Hello, DasRabbit!

    Since you're having trouble with this problem,
    . . I thought some baby-steps might be in order.



    \text{Solve for }x\!:\;\;-3\sqrt{x+4} + 10 \:=\:7
    We have:

    . . \text{-}3\sqrt{x+4} + 10 \:=\:7


    Subtract 10 from both sides:

    . . \text{-}3\sqrt{x+4} + 10 \:{\color{red}-\: 10} \:=\:7 \:{\color{red}-\: 10}\quad\Rightarrow\quad \text{-}3\sqrt{x+4} \:=\:\text{-}3


    Divide both sides by -3:

    . . \frac{\text{-}3\sqrt{x+4}}{{\color{red}\text{-}3}} \:=\:\frac{\text{-}3}{{\color{red}\text{-}3}} \quad\Rightarrow\quad \sqrt{x+4} \:=\:1


    Square both sides:

    . . (\sqrt{x+4})^{\color{red}2} \:=\: (1)^{\color{red}2} \quad\Rightarrow\quad x + 4 \:=\:1


    Subtract 4 from both sides:

    . . x + 4 \:{\color{red}-\: 4} \:=\:1 \:{\color{red}-\: 4} \quad\Rightarrow\quad \boxed{x \:=\:\text{-}3}
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