im not good at math :( *hmph*

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[x^2(2lnx)] + [(lnx)(lnx)3x^2]=0

exact values of x; no calculator approximations.

im hopeless at these type of questions.
If I'm reading it right, it would simplify to:

x^2(lnx) [2 + 3ln(x)] = 0

In which case you need x^2(lnx) = 0 or you need 2 + 3ln(x) = 0.

For the former you need either x^2 = 0 (so x = 0) or ln(x) = 0 (so x = 1).

For the latter you need ln(x) = -2/3 which means you need x such that x = e^(-2/3). If you can do that in your head, God bless you. 0.5134 is approximately the answer for that one. The best I can offer on that is knowing that e = 2.71 so you'd need 1/(2.71)^2/3. If you square 2.71 you'd probably get between 7 and 8. If you cube root that you'd probably get something near 2, I'd guess 1.9 or so. So 1/1.9 is pretty close to 1/2 which is 0.5, so I would go for the answer just above 0.5.
 
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