$$x^2(\frac{1}{10})^2+(1-x)^2(\frac{4}{10})^2 = (\frac{2}{10})^2$$

$$ \begin{aligned} x^2(\frac{1}{10})^2+(1-x)^2(\frac{4}{10})^2 &= (\frac{2}{10})^2&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x^2(\frac{1}{10})^2+10(1-x)^2(\frac{4}{10})^2 &= 10(\frac{2}{10})^2&& \text{cancel out the denominators} \\[1 em]0+10(1-x)^2\cdot0.16 &= 0&& \text{simplify left side} \\[1 em]0+10(1-2x+x^2)\cdot0.16 &= 0&& \\[1 em]0+(10-20x+10x^2)\cdot0.16 &= 0&& \\[1 em]0+0+0x+0x^2 &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$

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