Question
$$\frac{36}{x}+x = 6$$
Answer
$$ \begin{matrix}x_1 = 3+3 \sqrt{ 3 }i & x_2 = 3-3 \sqrt{ 3 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{36}{x}+x &= 6&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{36}{x}+xx &= x\cdot6&& \text{cancel out the denominators} \\[1 em]36+x^2 &= 6x&& \text{simplify left side} \\[1 em]x^2+36 &= 6x&& \text{move all terms to the left hand side } \\[1 em]x^2+36-6x &= 0&& \text{simplify left side} \\[1 em]x^2-6x+36 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-6x+36 = 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.
This page was created using
Polynomial Equations Solver