$$\frac{1}{x^2} = \frac{1}{169}$$
Answer
$$ \begin{matrix}x_1 = 13 & x_2 = -13 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x^2} &= \frac{1}{169}&& \text{multiply ALL terms by } \color{blue}{ x^2\cdot169 }. \\[1 em]x^2\cdot169\cdot\frac{1}{x^2} &= x^2\cdot169\cdot\frac{1}{169}&& \text{cancel out the denominators} \\[1 em]169 &= x^2&& \text{move all terms to the left hand side } \\[1 em]169-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2+169 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+169 = 0 $ is a quadratic equation.
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