$$x^2+2^{1/2}x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 3 }}{ 2 }i & x_2 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 3 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+2^{1/2}x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x^2+22^{1/2}x+2\cdot1 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2+2x+2 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+2x+2 = 0 $ is a quadratic equation.
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