Finite Math Examples

$x^{3} + 5 = 0$

Step 1

Subtract $5$ from both sides of the equation.

$x^{3} = - 5$

Step 2

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

$x = \sqrt[3]{- 5}$

Step 3

Simplify $\sqrt[3]{- 5}$ .

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Step 3.1

Rewrite $- 5$ as ${(- 1)}^{3} \cdot 5$ .

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Step 3.1.1

Rewrite $- 5$ as $- 1 (5)$ .

$x = \sqrt[3]{- 1 (5)}$

Step 3.1.2

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

$x = \sqrt[3]{{(- 1)}^{3} \cdot 5}$

Step 3.2

Pull terms out from under the radical.

$x = - 1 \sqrt[3]{5}$

Step 3.3

Rewrite $- 1 \sqrt[3]{5}$ as $- \sqrt[3]{5}$ .

$x = - \sqrt[3]{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[3]{5}$

Decimal Form:

$x = - 1.70997594 \dots$

Step 5