Question

Solve for $x:x^2+2\sqrt{3}x+3=0$.

Answer 1

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

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

$x(x+\sqrt{3})+\sqrt{3}(x+\sqrt{3})=0$

$(x+\sqrt{3})(x+\sqrt{3})=0$

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

$x=-\sqrt{3},-\sqrt{3}$

$\therefore x=-\sqrt{3}$