Solve this:
Q). $f\left(x\right)=4\sqrt{3}{x}^2+5x-2\sqrt{3}$

Dear student
Since it is not mentioned in the question what to find so according to my knowledge I am simplifying f(x) by completing the square method.
$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=4\sqrt{3}{\mathrm{x}}^2+5\mathrm{x}-2\sqrt{3} \\ ={\mathrm{x}}^2+\frac{5\mathrm{x}}{4\sqrt{3}}-\frac{2\sqrt{3}}{4\sqrt{3}} \\ ={\mathrm{x}}^2+\frac{5\mathrm{x}}{4\sqrt{3}}-\frac{1}{2} \\ ={\mathrm{x}}^2+\frac{5\mathrm{x}}{4\sqrt{3}}+{\left(\frac{5}{8\sqrt{3}}\right)}^2-{\left(\frac{5}{8\sqrt{3}}\right)}^2-\frac{1}{2} \\ ={\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^2-\frac{25}{192}-\frac{1}{2} \\ ={\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^2-\frac{121}{192} \end{gathered}$$