Find All Complex Solutions 5x^6=30

$5 x^{6} = 30$

Subtract $30$ from both sides of the equation.

$5 x^{6} - 30 = 0$

Factor $5$ out of $5 x^{6} - 30$ .

Factor $5$ out of $5 x^{6}$ .

$5 (x^{6}) - 30 = 0$

Factor $5$ out of $- 30$ .

$5 x^{6} + 5 \cdot - 6 = 0$

Factor $5$ out of $5 x^{6} + 5 \cdot - 6$ .

$5 (x^{6} - 6) = 0$

Divide each term in $5 (x^{6} - 6) = 0$ by $5$ and simplify.

Divide each term in $5 (x^{6} - 6) = 0$ by $5$ .

$\frac{5 (x^{6} - 6)}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (x^{6} - 6)}{5} = \frac{0}{5}$

Divide $x^{6} - 6$ by $1$ .

$x^{6} - 6 = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x^{6} - 6 = 0$

Add $6$ to both sides of the equation.

$x^{6} = 6$

Take the 6th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[6]{6}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt[6]{6}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt[6]{6}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt[6]{6}, - \sqrt[6]{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[6]{6}, - \sqrt[6]{6}$

Decimal Form:

$x = 1.34800615 \dots, - 1.34800615 \dots$