# Isolating a variable with a square root

• Sep 29th 2012, 01:58 PM
DasRabbit
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?
http://www.imathas.com/cgi-bin/mimet...}%2B{10}%3D{7} for http://www.imathas.com/cgi-bin/mimetex.cgi?{x}
• Sep 29th 2012, 03:15 PM
Plato
Re: Isolating a variable with a square root
Quote:

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?
http://www.imathas.com/cgi-bin/mimet...}%2B{10}%3D{7} for http://www.imathas.com/cgi-bin/mimetex.cgi?{x}

\begin{align*} -3\sqrt{x+4} &= -3 \\ \sqrt{x+4} &= 1 \\x+4 &= 1 \end{align*}
• Sep 29th 2012, 03:22 PM
Soroban
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.

Quote:

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

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