Question
$$2x\cdot9+\frac{1}{x}+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 36 }+\dfrac{\sqrt{ 71 }}{ 36 }i & x_2 = -\dfrac{ 1 }{ 36 }-\dfrac{\sqrt{ 71 }}{ 36 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x\cdot9+\frac{1}{x}+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x2x\cdot9+x\cdot\frac{1}{x}+x\cdot1 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]18x^2+1+x &= 0&& \text{simplify left side} \\[1 em]18x^2+x+1 &= 0&& \\[1 em] \end{aligned} $$
$ 18x^{2}+x+1 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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