Solve for x x^6+1=0

$x^{6} + 1 = 0$

Subtract $1$ from both sides of the equation.

$x^{6} = - 1$

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

$x = \pm \sqrt[6]{- 1}$

Simplify $\pm \sqrt[6]{- 1}$ .

Rewrite $- 1$ as $i^{6}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm i$

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.

$x = i$

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

$x = - i$

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

$x = i, - i$