Finite Math Examples

$x^{3} + i = 0$

Step 1

Subtract $i$ from both sides of the equation.

$x^{3} = - i$

Step 2

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

$x = \sqrt[3]{- i}$

Step 3

Simplify $\sqrt[3]{- i}$ .

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Step 3.1

Rewrite $- i$ as ${({(- 1)}^{3})}^{3} i$ .

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Step 3.1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$x = \sqrt[3]{{(- 1)}^{3} i}$

Step 3.1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$x = \sqrt[3]{{({(- 1)}^{3})}^{3} i}$

Step 3.2

Pull terms out from under the radical.

$x = {(- 1)}^{3} \sqrt[3]{i}$

Step 3.3

Raise $- 1$ to the power of $3$ .

$x = - \sqrt[3]{i}$

Step 4