<s>[INST] How do you solve for x in this equation? I tried expanding, but I still can't get rid of the exponents to isolate x. 
$$\frac{(1+x)^4-1}{x}=4.374616$$
Thank you in advance for your help. 
 [/INST] \begin{align}
(1+x)^{4} - 1 &= [(1+x)^{2} - 1] [ (1+x)^{2} + 1] = (1+x-1)(1+x+1)(x^{2} + 2x +1)
\nonumber\\
&= x(x+2)(x^{2}+2x+2)
\end{align}
or
\begin{align}
\frac{(1+x)^{4} -1}{x} = (x+2) (x^{2} + 2x +2).
\end{align}
Now, $4.374616$ can be factored into 
\begin{align}
4.374616 = (2.06)(2.1236) = (2 + .06)((.06)^{2} + 2(.06) + 2).
\end{align}
This yields
\begin{align}
(x+2) (x^{2} + 2x +2) = (2 + .06)((.06)^{2} + 2(.06) + 2)
\end{align}
which gives $x = .06$. 
</s>