Calculus Examples

$0 = 10 x^{3} - 116640$

Step 1

Rewrite the equation as $10 x^{3} - 116640 = 0$ .

$10 x^{3} - 116640 = 0$

Step 2

Add $116640$ to both sides of the equation.

$10 x^{3} = 116640$

Step 3

Subtract $116640$ from both sides of the equation.

$10 x^{3} - 116640 = 0$

Step 4

Factor $10$ out of $10 x^{3} - 116640$ .

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Step 4.1

Factor $10$ out of $10 x^{3}$ .

$10 (x^{3}) - 116640 = 0$

Step 4.2

Factor $10$ out of $- 116640$ .

$10 x^{3} + 10 \cdot - 11664 = 0$

Step 4.3

Factor $10$ out of $10 x^{3} + 10 \cdot - 11664$ .

$10 (x^{3} - 11664) = 0$

Step 5

Divide each term in $10 (x^{3} - 11664) = 0$ by $10$ and simplify.

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Step 5.1

Divide each term in $10 (x^{3} - 11664) = 0$ by $10$ .

$\frac{10 (x^{3} - 11664)}{10} = \frac{0}{10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{10 (x^{3} - 11664)}{10} = \frac{0}{10}$

Step 5.2.1.2

Divide $x^{3} - 11664$ by $1$ .

$x^{3} - 11664 = \frac{0}{10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $10$ .

$x^{3} - 11664 = 0$

Step 6

Add $11664$ to both sides of the equation.

$x^{3} = 11664$

Step 7

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

$x = \sqrt[3]{11664}$

Step 8

Simplify $\sqrt[3]{11664}$ .

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Step 8.1

Rewrite $11664$ as $18^{3} \cdot 2$ .

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Step 8.1.1

Factor $5832$ out of $11664$ .

$x = \sqrt[3]{5832 (2)}$

Step 8.1.2

Rewrite $5832$ as $18^{3}$ .

$x = \sqrt[3]{18^{3} \cdot 2}$

Step 8.2

Pull terms out from under the radical.

$x = 18 \sqrt[3]{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = 18 \sqrt[3]{2}$

Decimal Form:

$x = 22.67857889 \dots$