Question

Solve the following equation by using the method of completing the square:
$\sqrt{3}{x}^2+10x+7\sqrt{3}=0$

Answer 1

$\sqrt{3}{x}^2+10x+7\sqrt{3}=0$

$x^2+\frac{10}{\sqrt{3}}+7$= 0

$x^2+\frac{10}{\sqrt{3}}$=-7

Third term = $(\frac{1}{2}\times coefficientofx{)}^2$

= $(\frac{1}{2}\times \frac{10}{\sqrt{3}}{)}^2$

= $(\frac{5}{\sqrt{3}}{)}^2$

=$\frac{25}{3}$

Therefore,

$x^2+\frac{10}{\sqrt{3}}$ + $\frac{25}{3}$=-7 + $\frac{25}{3}$.. (adding to both sides)

$x^2+\frac{10}{\sqrt{3}}$ + $\frac{25}{3}$ = $\frac{4}{3}$.

( x - $\frac{5}{\sqrt{3}}$.) =± $\frac{2}{\sqrt{3}}$ ... (taking square roots)

Hence,

x = $\frac{7}{\sqrt{3}}$ ,√3