Question
$$x^2-\frac{4}{10}x+\frac{13}{100} = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 5 }+\dfrac{ 3 }{ 10 }i & x_2 = \dfrac{ 1 }{ 5 }-\dfrac{ 3 }{ 10 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2-\frac{4}{10}x+\frac{13}{100} &= 0&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100x^2-100 \cdot \frac{4}{10}x+100\cdot\frac{13}{100} &= 100\cdot0&& \text{cancel out the denominators} \\[1 em]100x^2-40x+13 &= 0&& \\[1 em] \end{aligned} $$
$ 100x^{2}-40x+13 = 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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