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# Help with solving math problem with chemistry 'small approximation'

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( (2x)^2 / (.901-x) ) = 2.25 , x = ?

So the answer is x = 0.4842

But I can't get this value by using a basic Ti 36 Pro.

I tried to apply the small appromixation, which would reduce the equation down to -> ((2x)^2 / .901) = 2.25

2x^2 becomes 4x^2 / .901 = 2.25

Move .901 over -> 4x^2 = 2.25*.901

Divide by 4 -> x^2 = (2.25*.901)/4

Then square root both sides to isolate x -> x = sqr((2.24*.901)/4)

I got x= +- 0.71

Either I'm wrong or my Chemistry prof is wrong

Guest Apr 13, 2017
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#1
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( (2x)^2 / (.901-x) ) = 2.25        multiply both sides by  .901 - x

(2x)^2   =  2.25 (.901 - x)     simplify

4x^2   = 2.02725  - 2.25x     rearrange as

4x^2 + 2.25x - 2.02725  = 0

Here's are WolframAlpha's solutions for this :

https://www.wolframalpha.com/input/?i=4x%5E2+%2B+2.25x+-+2.02725+%C2%A0%3D+0

CPhill  Apr 13, 2017

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