# 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.
$\mathrm{f}\left(\mathrm{x}\right)=4\sqrt{3}{\mathrm{x}}^{2}+5\mathrm{x}-2\sqrt{3}\phantom{\rule{0ex}{0ex}}={\mathrm{x}}^{2}+\frac{5\mathrm{x}}{4\sqrt{3}}-\frac{2\sqrt{3}}{4\sqrt{3}}\phantom{\rule{0ex}{0ex}}={\mathrm{x}}^{2}+\frac{5\mathrm{x}}{4\sqrt{3}}-\frac{1}{2}\phantom{\rule{0ex}{0ex}}={\mathrm{x}}^{2}+\frac{5\mathrm{x}}{4\sqrt{3}}+{\left(\frac{5}{8\sqrt{3}}\right)}^{2}-{\left(\frac{5}{8\sqrt{3}}\right)}^{2}-\frac{1}{2}\phantom{\rule{0ex}{0ex}}={\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^{2}-\frac{25}{192}-\frac{1}{2}\phantom{\rule{0ex}{0ex}}={\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^{2}-\frac{121}{192}$

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What are you looking for?