Question
$$x+(100-x)x+x = 100$$
Answer
$$ \begin{matrix}x_1 = 51-\sqrt{ 2501 } & x_2 = 51+\sqrt{ 2501 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+(100-x)x+x &= 100&& \text{simplify left side} \\[1 em]x+100x-x^2+x &= 100&& \\[1 em]-x^2+101x+x &= 100&& \\[1 em]-x^2+102x &= 100&& \text{move all terms to the left hand side } \\[1 em]-x^2+102x-100 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+102x-100 = 0 $ is a quadratic equation.
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