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I'm looking to solve this equation mentally, with the following numbers, using an algebra shortcut. $a = bc + \frac{1}{2} dc^2$ with
$ \begin{eqnarray*} c &=& 10.204, \\ d &=& -9.8, \\ b &=& 100. \end{eqnarray*} $ Can anyone think of a shortcut that would make solving this easier?

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    Xaav, To clarify, I did not do it. I was in fact requesting for such an explanation. Also, I think this question is interesting and within the scope of the site.2011-09-05

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HINT $\ $ Since $\rm\ \ d\:c\ \approx\ (0.2+10)\:(0.2-10)\ =\ 0.04-100\:,\ $ we conclude that

$\rm\ \ c\ (b+dc/2)\ \approx\ 10.2 * (100 + (0.04-100)/2)\ \approx\ 10.2 * (50 + 0.02)\ \approx\ 510.204$

The above mental approximation is very close to the actual value - which is $\ \: 510.20404$