$$ \begin{aligned} 1^2 &= 1+x&& \text{simplify left and right hand side} \\[1 em]1 &= x+1&& \text{ swap the left and right side of the equation } \\[1 em]x+1 &= 1&& \text{ move 1 to the right } \\[1 em]x &= 1-1&& \\[1 em]x &= 0&& \text{ divide both sides by $ 1 $ } \\[1 em]x &= \frac{0}{1}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$
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