$$ \begin{aligned} 1(x-3)(x-3)+1 &= 0&& \text{simplify left side} \\[1 em](x-3)(x-3)+1 &= 0&& \\[1 em]x^2-3x-3x+9+1 &= 0&& \\[1 em]x^2-6x+10 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-6x+10 = 0 $ is a quadratic equation.
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