Algebra Examples

$x^{3} = - 21$

Step 1

Add $21$ to both sides of the equation.

$x^{3} + 21 = 0$

Step 2

Subtract $21$ from both sides of the equation.

$x^{3} = - 21$

Step 3

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

$x = \sqrt[3]{- 21}$

Step 4

Simplify $\sqrt[3]{- 21}$ .

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Step 4.1

Rewrite $- 21$ as ${(- 1)}^{3} \cdot 21$ .

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Step 4.1.1

Rewrite $- 21$ as $- 1 (21)$ .

$x = \sqrt[3]{- 1 (21)}$

Step 4.1.2

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

$x = \sqrt[3]{{(- 1)}^{3} \cdot 21}$

Step 4.2

Pull terms out from under the radical.

$x = - 1 \sqrt[3]{21}$

Step 4.3

Rewrite $- 1 \sqrt[3]{21}$ as $- \sqrt[3]{21}$ .

$x = - \sqrt[3]{21}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[3]{21}$

Decimal Form:

$x = - 2.75892417 \dots$