Trigonometry Examples

${(v + 7)}^{3} + 88 = 0$

Step 1

Subtract $88$ from both sides of the equation.

${(v + 7)}^{3} = - 88$

Step 2

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

$v + 7 = \sqrt[3]{- 88}$

Step 3

Simplify $\sqrt[3]{- 88}$ .

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Step 3.1

Rewrite $- 88$ as ${(- 2)}^{3} \cdot 11$ .

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Step 3.1.1

Factor $- 8$ out of $- 88$ .

$v + 7 = \sqrt[3]{- 8 (11)}$

Step 3.1.2

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

$v + 7 = \sqrt[3]{{(- 2)}^{3} \cdot 11}$

Step 3.2

Pull terms out from under the radical.

$v + 7 = - 2 \sqrt[3]{11}$

Step 4

Subtract $7$ from both sides of the equation.

$v = - 2 \sqrt[3]{11} - 7$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = - 2 \sqrt[3]{11} - 7$

Decimal Form:

$v = - 11.44796018 \dots$