Question

Solve each of the following equation by using the method of completing the square:
$4x^2+4\sqrt{3}x+3=0$ ?

Answer 1

$4x^2+4\sqrt{3x}+3=0$

Dividing by $4$

$x^2+\sqrt{3x}+\frac{3}{4}=0$

$x^2+\sqrt{3x}=-\frac{3}{4}$

Third term $={(\frac{1}{2}\times \sqrt{3})}^2=\frac{3}{4}$

adding $\frac{3}{4}$ on both sides

$x^2+\sqrt{3x}+\frac{3}{4}=-\frac{3}{4}+\frac{3}{4}$

$x^2+\sqrt{3x}+\frac{3}{4}=0$

$x+\sqrt{\frac{3}{2}}=0$ or $x=-\sqrt{\frac{3}{2}}$