Question

Solve each of the following equations by using the method of completing the square:

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

Answer 1

$$\begin{gathered} 4x^2+4\sqrt{3}x+3=0 \\ \Rightarrow 4x^2+4\sqrt{3}x=-3 \\ \Rightarrow {\left(2x\right)}^2+2\times 2x\times \sqrt{3}+{\left(\sqrt{3}\right)}^2=-3+{\left(\sqrt{3}\right)}^2\left[\mathrm{Adding}{\left(\sqrt{3}\right)}^2\mathrm{on}\mathrm{both}\mathrm{sides}\right] \\ \Rightarrow {\left(2x+\sqrt{3}\right)}^2=-3+3=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow 2x+\sqrt{3}=0 \\ \Rightarrow x=-\frac{\sqrt{3}}{2} \end{gathered}$$
Hence, $-\frac{\sqrt{3}}{2}$ is the repeated root of the given equation.