Question 256500
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 115.4\ =\ \left(\frac{19600}{8m}\right)\ +\ \left(\frac{m}{2}\right)]


First reduce the very ugly fraction in the first term of the RHS:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 115.4\ =\ \left(\frac{2450}{m}\right)\ +\ \left(\frac{m}{2}\right)]


Multiply both sides by *[tex \Large 10m] to get the *[tex \Large m] out of the denominator in the first term of the RHS and to get rid of the decimal coefficient in the LHS.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1154m\ =\ 24500\ +\ 5m^2]


Put the quadratic into standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5m^2\ -\ 1154m\ +\ 24500\ =\ 0]


This does not factor over the rationals, so use the quadratic formula to solve.  There will be two real number roots since the discriminant is positive.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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