Question

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

[4 marks]

Answer 1

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

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

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

Third term = $(\frac{1}{2}\times$ coefficient of $x{)}^2$

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

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

=$\frac{25}{3}$ (2 Marks)

Therefore,

$x^2+\frac{10}{\sqrt{3}}x$ + $\frac{25}{3}=-7+\frac{25}{3}$

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

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

Hence,

x = $\frac{-7}{\sqrt{3}},-\sqrt{3}$ (2 Marks)