# How do you solve 7- sqrt(x-6)=3 and find any extraneous solutions?

Feb 28, 2017

First, subtract $\textcolor{red}{7}$ from each side of the equation to isolate the square root expression while keeping the equation balanced:

$- \textcolor{red}{7} + 7 - \sqrt{x - 6} = - \textcolor{red}{7} + 3$

$0 - \sqrt{x - 6} = - 4$

$- \sqrt{x - 6} = - 4$

Next, multiply each side of the equation by $\textcolor{red}{- 1}$ to eliminate the negative terms while keeping the equation balanced:

$\textcolor{red}{- 1} \times - \sqrt{x - 6} = \textcolor{red}{- 1} \times - 4$

$\sqrt{x - 6} = 4$

Then, square both sides of the equation to eliminate the square root function while keeping the equation balanced:

${\left(\sqrt{x - 6}\right)}^{2} = {4}^{2}$

$x - 6 = 16$

Now, add $\textcolor{red}{6}$ to each side of the equation to solve for $x$ while keeping the equation balanced:

$x - 6 + \textcolor{red}{6} = 16 + \textcolor{red}{6}$

$x - 0 = 22$

$x = 22$

An extraneous solution would be $\sqrt{x - 6} = - 4$