Answer
$x=0.826$ or $x=-0.807$
Work Step by Step
$5.25x^6-0.2x^3-1.55=0$
Let $x^3=a$.
$5.25a^2-0.2a-1.55=0$
Multiplying both sides of the equation by 100:
$525a^2-20a-155=0$
Using the quadratic formula for the quadratic equation.
$a=\frac{20\pm \sqrt{(20)^2+4(525)(155)}}{2\times525}=\frac{20 \pm \sqrt{325900}}{1050}$
Thus, $a=0.563$ or $a=-0.525$.
Since $x^3=a$, $x=\sqrt[3] {0.563}=0.826$ or $x=\sqrt[3] {-0.525}=-0.807$
