Isolating a variable with a square root

**DasRabbit** · September 29th 2012, 01:58 PM

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?
$-{3}\sqrt{{{x}+{4}}}+{10}={7}$ for ${x}$

**Plato** · September 29th 2012, 03:15 PM

Originally Posted by DasRabbit

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?
$-{3}\sqrt{{{x}+{4}}}+{10}={7}$ for ${x}$

$\begin{align*} -3\sqrt{x+4} &= -3 \\ \sqrt{x+4} &= 1 \\x+4 &= 1 \end{align*}$

**Soroban** · September 29th 2012, 03:22 PM

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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