Algebra Examples

$F (x) = x^{3} + 2$

Step 1

Set $x^{3} + 2$ equal to $0$ .

$x^{3} + 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $2$ from both sides of the equation.

$x^{3} = - 2$

Step 2.2

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

$x = \sqrt[3]{- 2}$

Step 2.3

Simplify $\sqrt[3]{- 2}$ .

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Step 2.3.1

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

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Step 2.3.1.1

Rewrite $- 2$ as $- 1 (2)$ .

$x = \sqrt[3]{- 1 (2)}$

Step 2.3.1.2

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

$x = \sqrt[3]{{(- 1)}^{3} \cdot 2}$

Step 2.3.2

Pull terms out from under the radical.

$x = - 1 \sqrt[3]{2}$

Step 2.3.3

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

$x = - \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[3]{2}$

Decimal Form:

$x = - 1.25992104 \dots$

Step 4