Question

Solve 2✓3x²-5x-✓3=0 by the method of completing square.

Answer 1

$2\sqrt{3}x^2-5x-\sqrt{3}=0$

$x^2-\frac{5}{2\sqrt{3}}x-\frac{\sqrt{3}}{2\sqrt{3}}=0$

$x^2-\frac{5}{2\sqrt{3}}x-\frac{1}{2}=0$

$x^2-2*\frac{5}{4\sqrt{3}}x+\frac{25}{3*16}-\frac{25}{3*16}-\frac{1}{2}=0$

$(x-\frac{5}{2\sqrt{3}})^2-(\frac{25}{3*16}+\frac{1}{2})=0$

$(x-\frac{5}{2\sqrt{3}})^2-(\frac{25+24}{48})=0$

$(x-\frac{5}{2\sqrt{3}})^2=\frac{49}{48}$

$x-\frac{5}{2\sqrt{3}}=\frac{7}{4\sqrt{3}}$ or, $x-\frac{5}{2\sqrt{3}}=-\frac{7}{4\sqrt{3}}$

$x=\frac{7}{4\sqrt{3}}+\frac{5}{2\sqrt{3}}$ or, $x=-\frac{7}{4\sqrt{3}}+\frac{5}{2\sqrt{3}}$

$x=\frac{17}{4\sqrt{3}}$ or,$x=\frac{3}{4\sqrt{3}}$