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e^17.3 * x / (x + 237.3) = 0.013 * (x + 273.2)

Guest Feb 27, 2017
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 #1
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e^17.3 * x / (x + 237.3) = 0.013 * (x + 273.2)

 

\(\frac{e^{17.3} \times x }{ (x + 237.3) }= 0.013 (x + 273.2)\\ e^{17.3} \times x = 0.013 (x + 273.2)(x + 237.3) \\\)

Just expand it all out, take it all to one side ie make =0

 

then solve using the quadratic formula :)

Melody  Feb 27, 2017
 #2
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Solve for x:
0.013 (x + 237.3) (x + 273.2) = 3.26058×10^7 x

Expand out terms of the left hand side:
0.013 x^2 + 6.6365 x + 842.795 = 3.26058×10^7 x

Subtract 3.26058×10^7 x from both sides:
0.013 x^2 - 3.26058×10^7 x + 842.795 = 0

x = (3.26058×10^7 ± sqrt((-3.26058×10^7)^2 - 4×0.013×842.795))/0.026 = (3.26058×10^7 ± sqrt(1.06314×10^15))/0.026 = (3.26058×10^7 ± 3.26058×10^7)/0.026 = 1.25407×10^9 ± 1.25407×10^9:
x = 2.50814×10^9 or x = 0.0000259338

0.013 (x + 237.3) (x + 273.2) ⇒ 0.013 (237.3 + 0.0000259338) (273.2 + 0.0000259338) ≈ 842.795
3.26058×10^7 x ⇒ 3.26058×10^7 0.0000259338 ≈ 845.59:
So this solution is incorrect

0.013 (x + 237.3) (x + 273.2) ⇒ 0.013 (237.3 + 2.50814×10^9) (273.2 + 2.50814×10^9) ≈ 8.17797×10^16
3.26058×10^7 x ⇒ 3.26058×10^7 2.50814×10^9 ≈ 8.17797×10^16:
So this solution is incorrect

All the solutions are incorrect:
Answer: | NO SOLUTIONS!!

Guest Feb 27, 2017

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