Solve (x)(x^3-x-8)=0

$$( x ) ( x ^ { 3 } - x - 8 ) = 0$$

Solve for x

$$x = \frac{9 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{1293} + 36} + \sqrt[3]{36 - \sqrt{1293}})}}{9} \approx 2.166312747$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x^{3}-x-8.

$$x^{4}-x^{2}-8x=0$$

Substitute t for x^{2}.

$$t^{2}-t-8=0$$

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, -1 for b, and -8 for c in the quadratic formula.

$$t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-8\right)}}{2}$$

Do the calculations.

$$t=\frac{1±\sqrt{33}}{2}$$

Solve the equation t=\frac{1±\sqrt{33}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{33}+1}{2} t=\frac{1-\sqrt{33}}{2}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.

$$x=\frac{\sqrt{2\sqrt{33}+2}}{2} x=-\frac{\sqrt{2\sqrt{33}+2}}{2}$$