Answer
$m=\left\{ \dfrac{1-\sqrt{7}}{3},\dfrac{1+\sqrt{7}}{3} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(3x-1)^2=7
,$ take the square root of both sides (Square Root Property). Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
3x-1=\pm\sqrt{7}
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
3x=1\pm\sqrt{7}
\\\\
x=\dfrac{1\pm\sqrt{7}}{3}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=\dfrac{1-\sqrt{7}}{3}
\\\\\text{OR}\\\\
x=\dfrac{1+\sqrt{7}}{3}
.\end{array}
Hence, $
m=\left\{ \dfrac{1-\sqrt{7}}{3},\dfrac{1+\sqrt{7}}{3} \right\}
.$
