Solve x^6-19x^3=216

$$x ^ { 6 } - 19 x ^ { 3 } = 216$$

Solve for x

$$x=-2$$

$$x=3$$

Steps Using the Quadratic Formula

Subtract 216 from both sides.

$$x^{6}-19x^{3}-216=0$$

Substitute t for x^{3}.

$$t^{2}-19t-216=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -19 for b, and -216 for c in the quadratic formula.

$$t=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 1\left(-216\right)}}{2}$$

Do the calculations.

$$t=\frac{19±35}{2}$$

Solve the equation t=\frac{19±35}{2} when ± is plus and when ± is minus.

$$t=27 t=-8$$

Since x=t^{3}, the solutions are obtained by evaluating x=\sqrt[3]{t} for each t.

$$x=3 x=-2$$