Monday, June 3, 2013

how to solve this equation? x + ln (x^(2+x)) = 0

First we rewrite 



ln+%28x%5E%282%2Bx%29%29+=+-x 
Immediately we notice that no matter what we do we end up with exponential/logarithmic term as well as algebraic terms. This equation cannot be solved using algebra because it is neither strictly algebraic nor exponential and so no operations can be done to solve directly for x. In cases like this we can use numerical or graphic methods: 

+graph%28+300%2C+300%2C+-1%2C+2%2C+-2%2C+2%2C+-x%2C+ln%28x%5E2%2Bx%29%29+ 


After tinkering with the window settings and such we can approximate the intersection as much as we need. 
x is about 0.75941 



:)

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