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September 16, 2014

September 16, 2014

Posted by **Sam** on Thursday, July 3, 2014 at 3:36pm.

Thanks in advance!

3x^2+4lnx+4=0

- Algebra -
**Steve**, Thursday, July 3, 2014 at 5:45pmThere's no algebraic way to do it. A numeric method or a graphical analysis will be required. See

http://www.wolframalpha.com/input/?i=solve+3x^2%2B4lnx%2B4%3D0

- Algebra -
**Reiny**, Thursday, July 3, 2014 at 5:46pmFor a complicated equation such as yours, the most powerful method is probably Newton's Method.

let y = 3x^2+4lnx+4

dy/dx = 6x + 4/x

newx = x - y/(dy/dx)

= x - (3x^2+4lnx+4)/(6x + 4/x)

which simplifies to

newx = (3x^2 - 4lnx)/(6x + 4/x)

now use an iteration process, I started with x = 1

x | newx

1 -- .3

.3 -- .336072..

.336072 -- .337716

.337716 -- .337719143

.337719143 -- .337719143

since the last x used returned the same value of x, we cannot improve on that answer.

Amazing that after only 4 interations, I got

x =.337719143 correct to 9 decimal places

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