Question

find the roots of the quadratic equation by using the method of completing the square
plz explain me easily
$4 x^{2} +4 \sqrt3x+3=0$

Answer 1

The identity to be used is (a+b)² = a² + 2ab + b²

$4 x^{2} + 4 \sqrt{3}x + 3=0\\ \\ \Rightarrow (2x)^2 + 2 \times 2x \times \sqrt{3}\ + (\sqrt{3} )^2=0 \\ \\\Rightarrow (2x+ \sqrt{3} )^2=0\\ \\ \Rightarrow 2x+ \sqrt{3}=0 \\ \\ \Rightarrow 2x=- \sqrt{3}\\ \\ \Rightarrow x=- \frac{ \sqrt{3} }{2}$