Answer
$x=\frac{1}{3}\pm\frac{4}{3}i$
Work Step by Step
$(3x-1)^2=-16$ Use the square root property.
$\sqrt(3x-1)^2=\pm\sqrt-16$
$3x-1=\pm4i$ The square root of a negative number yields a complex number, denoted as, $i$.
$3x=\pm4i+1$
$x=\frac{1}{3}\pm\frac{4}{3}i$
