Answer
$c \approx \pm1.24$
Work Step by Step
$96 -24c^{4} = 40$
$24(4 - c^{4}) = 40$
$4 - c^{4} = \frac{5}{3}$
$- c^{4} = - \frac{7}{3}$
$c^{4} = \frac{7}{3}$
$c = \pm(\frac{7}{3})^{\frac{1}{4}}$
by GDC / calculator
$c = \pm1.2359...$
$c \approx \pm1.24$
Check:
$96 - 24c^{4} \overset{?}{=} 40$
$96 - 24(\pm1.2359...)^{4} \overset{?}{=} 40$
$96 - 24(2.333...) \overset{?}{=} 40$
$96 - 56 \overset{?}{=} 40$
$40 = 40$
