Finding the limit of $\sqrt{4x^2+x+7}+2x$ I've been working on this problem for a while now, but I can't solve it  
$$\lim\limits_{x\to-\infty}{\sqrt{4x^2+x+7}+2x}$$
I've tried multiplying by 
$$\frac{\sqrt{4x^2+x+7}-2x}{\sqrt{4x^2+x+7}-2x}$$
but I didn't get it.  Am I missing something really obvious?  Can someone help me with this question?

$$
\begin{aligned}
\lim_{x\to-\infty}\left(\sqrt{4x^2+x+7}+2x\right) &= \lim_{x\to-\infty}\frac{4x^2+x+7-4x^2}{\sqrt{4x^2+x+7}-2x}\\
& =\lim_{x\to-\infty}\frac{x+7}{\sqrt{4x^2+x+7}-2x}\\
&=\lim_{x\to-\infty}\frac{-1-\frac{7}{x}}{\sqrt{4+\frac{1}{x}+\frac{7}{x^2}}+2}\\
&=-\frac{1}{4}
\end{aligned}
$$
