Let's begin by identifying key information given to us:
[tex]\begin{gathered} x^2=\frac{1}{49} \\ \text{Take the square root of both sides, we have:} \\ \sqrt[]{x^2}=\sqrt[]{\frac{1}{49}}\Rightarrow x=\sqrt[]{\frac{1^2}{7^2}} \\ \Rightarrow x=\pm\frac{1}{7} \\ \\ \therefore x=\pm\frac{1}{7} \end{gathered}[/tex]