# Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises - Page 511: 33

$m=\left\{ \dfrac{1-\sqrt{7}}{3},\dfrac{1+\sqrt{7}}{3} \right\}$

#### 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, $m=\left\{ \dfrac{1-\sqrt{7}}{3},\dfrac{1+\sqrt{7}}{3} \right\} .$

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