Sunday

December 21, 2014

December 21, 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

**Answer this Question**

**Related Questions**

Calculus - Find the derivative of y with respect to x. y= (lnx)/(3+4lnx) Should ...

Trig - Identies/equation, please help! - 2Sin(Θ+47°)=1 ΘЄ[0°, ...

Calc - Find the equation of a tangent line of a graph pf y=x^2+4lnx, which is ...

grammar - hello. is this statement correct in grammar: i think something is ...

algebra - I need to find the intercepts and then use them to graph the equation...

Algebra - 2(3x-6)-3(5x+4)=5(7x-8) For this equation, I keep getting ....

Chemistry - I'm trying do this question: 0.10 mol/L hydrochloric acid is ...

algebra - how do I find the vertex of y = x^2 - 18? I got -9, -81 but that seems...

Algebra - I know that standard form is Ax+By=C, but I'm not really sure how to ...

calculus - functions! - I was assigned this problem and I'm coming up against a ...