Question

4√3x² + 5x - 2√3 solve the quadratic equation by the method of completing the square

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}4\sqrt{3}{\mathrm{x}}^2+5\mathrm{x}-2\sqrt{3}=0 \\ \Rightarrow {\mathrm{x}}^2+\frac{5}{4\sqrt{3}}\mathrm{x}-\frac{1}{2}=0 \\ \Rightarrow {\mathrm{x}}^2+\frac{5}{4\sqrt{3}}\mathrm{x}+{\left(\frac{5}{8\sqrt{3}}\right)}^2-{\left(\frac{5}{8\sqrt{3}}\right)}^2-\frac{1}{2}=0 \\ \Rightarrow {\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^2-\frac{25}{192}-\frac{1}{2}=0 \\ \Rightarrow {\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^2=\frac{25}{192}+\frac{1}{2} \\ \Rightarrow {\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^2=\frac{25+96}{192} \\ \Rightarrow {\left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)}^2=\frac{121}{192} \\ \Rightarrow \left(\mathrm{x}+\frac{5}{8\sqrt{3}}\right)=\pm \frac{11}{8\sqrt{3}} \\ \Rightarrow \mathrm{x}=\pm \frac{11}{8\sqrt{3}}-\frac{5}{8\sqrt{3}} \\ \Rightarrow \mathrm{x}=-\frac{2}{\sqrt{3}}\mathrm{or}\mathrm{x}=\frac{3}{4\sqrt{3}} \end{gathered}$$
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