# How do you solve for x in r = sqrts/t?

Sep 7, 2017

See a solution process below:

#### Explanation:

If you are looking solve for $s$:

First, multiply each side of the equation by $\textcolor{red}{t}$ to isolate the $s$ term while keeping the equation balanced:

$r \cdot \textcolor{red}{t} = \frac{\sqrt{s}}{t} \cdot \textcolor{red}{t}$

$r t = \frac{\sqrt{s}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{t}}}} \cdot \cancel{\textcolor{red}{t}}$

$r t = \sqrt{s}$

Now, square both sides of the equation to solve for $s$ while keeping the equation balanced:

${\left(r t\right)}^{2} = {\left(\sqrt{s}\right)}^{2}$

${r}^{2} {t}^{2} = s$

$s = {r}^{2} {t}^{2}$

If you are looking solve for $t$:

Multiply both sides of the equation by $\frac{\textcolor{red}{t}}{\textcolor{b l u e}{r}}$ to solve for $t$ while keeping the equation balanced:

$r \cdot \frac{\textcolor{red}{t}}{\textcolor{b l u e}{r}} = \frac{\sqrt{s}}{t} \cdot \frac{\textcolor{red}{t}}{\textcolor{b l u e}{r}}$

$\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{r}}} \cdot \frac{\textcolor{red}{t}}{\cancel{\textcolor{b l u e}{r}}} = \frac{\sqrt{s}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{t}}}} \cdot \frac{\cancel{\textcolor{red}{t}}}{\textcolor{b l u e}{r}}$

$t = \frac{\sqrt{s}}{r}$