Finite Math Examples

${(u + 8)}^{3} + 24 = 0$

Step 1

Subtract $24$ from both sides of the equation.

${(u + 8)}^{3} = - 24$

Step 2

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

$u + 8 = \sqrt[3]{- 24}$

Step 3

Simplify $\sqrt[3]{- 24}$ .

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Step 3.1

Rewrite $- 24$ as ${(- 2)}^{3} \cdot 3$ .

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Step 3.1.1

Factor $- 8$ out of $- 24$ .

$u + 8 = \sqrt[3]{- 8 (3)}$

Step 3.1.2

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$u + 8 = \sqrt[3]{{(- 2)}^{3} \cdot 3}$

Step 3.2

Pull terms out from under the radical.

$u + 8 = - 2 \sqrt[3]{3}$

Step 4

Subtract $8$ from both sides of the equation.

$u = - 2 \sqrt[3]{3} - 8$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = - 2 \sqrt[3]{3} - 8$

Decimal Form:

$u = - 10.88449914 \dots$