Question
$$x+(1-x)x+x = 100$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 391 }}{ 2 }i & x_2 = \dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 391 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+(1-x)x+x &= 100&& \text{simplify left side} \\[1 em]x+x-x^2+x &= 100&& \\[1 em]-x^2+2x+x &= 100&& \\[1 em]-x^2+3x &= 100&& \text{move all terms to the left hand side } \\[1 em]-x^2+3x-100 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+3x-100 = 0 $ is a quadratic equation.
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