## Precalculus: Mathematics for Calculus, 7th Edition

$x=0\pm\dfrac{\sqrt{3}}{3}i$
$3x^{2}+1=0$ Take the $1$ to the right side: $3x^{2}=-1$ Take the $3$ dividing to the right side of the equation: $x^{2}=-\dfrac{1}{3}$ Take the square root of both sides: $\sqrt{x^{2}}=\sqrt{-\dfrac{1}{3}}$ $x=\pm\sqrt{\dfrac{1}{3}}i=\pm\dfrac{1}{\sqrt{3}}i=\pm\dfrac{\sqrt{3}}{3}i$ The solution is $x=0\pm\dfrac{\sqrt{3}}{3}i$