Answer
$x = ±7$
Work Step by Step
$\frac{2.4x^{6}-19}{1000} = 282.3386$
$2.4x^{6} - 19 = 282338.6$
$2.4x^{6} = 282357.6$
$x^{6} = 117,649$
$x = ±(117,649)^{\frac{1}{6}}$
$x = ±7$
Check:
When $x= 7$
$\frac{2.4x^{6}-19}{1000} \overset{?}{=} 282.3386$
$\frac{2.4(7)^{6}-19}{1000} \overset{?}{=} 282.3386$
$\frac{2.4(117,649)-19}{1000} \overset{?}{=} 282.3386$
$\frac{282357.6-19}{1000} \overset{?}{=} 282.3386$
$\frac{282338.6}{1000} \overset{?}{=} 282.3386$
$282.3386 = 282.3386$
When $x = -7$
$\frac{2.4x^{6}-19}{1000} \overset{?}{=} 282.3386$
$\frac{2.4(-7)^{6}-19}{1000} \overset{?}{=} 282.3386$
$\frac{2.4(117,649)-19}{1000} \overset{?}{=} 282.3386$
$\frac{282357.6-19}{1000} \overset{?}{=} 282.3386$
$\frac{282338.6}{1000} \overset{?}{=} 282.3386$
$282.3386 = 282.3386$
