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