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%% Ein Beispiel der DANTE-Edition
%% Mathematiksatz mit LaTeX
%% 3. Auflage
%% Beispiel 10-04-4 auf Seite 218.
%% Copyright (C) 2018 Herbert Voss
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\begin{document}
\begin{align}
y&= 2x^2 -3x +5\nonumber\\
& \hphantom{= \ 2\left(x^2-\frac{3}{2}\,x\right. }\textcolor{blue}{%
\overbrace{\hphantom{+\left(\frac{3}{4}\right)^2- %
\left(\frac{3}{4}\right)^2}}^{=0}}\nonumber\\[-11pt]
&=2\left(\textcolor{red}{\underbrace{x^2-\frac{3}{2}\,x + \left(\frac{3}{4}\right)^2}}
\underbrace{-\left(\frac{3}{4}\right)^2 + \frac{5}{2}}\right)\\
&=2\left(\qquad\textcolor{red}{\left(x-\frac{3}{4}\right)^2}
\qquad + \ \frac{31}{16}\qquad\right)\nonumber\\
y\textcolor{blue}{{}-\frac{31}{8}}
&=2\left(x\textcolor{cyan}{{}-\frac{3}{4}}\right)^2
\Rightarrow S\left(\frac{3}{4}\right|\left.\frac{31}{8}\right)\nonumber
\end{align}
\end{document}
