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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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A downvote is useful only when accompanied by some comment explaining it :-). – Srivatsan Sep 5 '11 at 0:10
Can someone please explain why this question was downvoted? – xaav Sep 5 '11 at 1:54
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. – Srivatsan Sep 5 '11 at 2:01
up vote 6 down vote accepted

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 $\ \: 510.20404$

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