Calculus Examples

$0.004 x = \frac{7263}{x^{2}}$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x^{2}$

Step 1.2

The LCM of one and any expression is the expression.

$x^{2}$

Step 2

Multiply each term in $0.004 x = \frac{7263}{x^{2}}$ by $x^{2}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $0.004 x = \frac{7263}{x^{2}}$ by $x^{2}$ .

$0.004 x \cdot x^{2} = \frac{7263}{x^{2}} x^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.2.1.1

Move $x^{2}$ .

$0.004 (x^{2} x) = \frac{7263}{x^{2}} x^{2}$

Step 2.2.1.2

Multiply $x^{2}$ by $x$ .

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Step 2.2.1.2.1

Raise $x$ to the power of $1$ .

$0.004 (x^{2} x^{1}) = \frac{7263}{x^{2}} x^{2}$

Step 2.2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$0.004 x^{2 + 1} = \frac{7263}{x^{2}} x^{2}$

Step 2.2.1.3

Add $2$ and $1$ .

$0.004 x^{3} = \frac{7263}{x^{2}} x^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $x^{2}$ .

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Step 2.3.1.1

Cancel the common factor.

$0.004 x^{3} = \frac{7263}{x^{2}} x^{2}$

Step 2.3.1.2

Rewrite the expression.

$0.004 x^{3} = 7263$

Step 3

Solve the equation.

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Step 3.1

Subtract $7263$ from both sides of the equation.

$0.004 x^{3} - 7263 = 0$

Step 3.2

Factor $0.004$ out of $0.004 x^{3} - 7263$ .

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Step 3.2.1

Factor $0.004$ out of $0.004 x^{3}$ .

$0.004 (x^{3}) - 7263 = 0$

Step 3.2.2

Factor $0.004$ out of $- 7263$ .

$0.004 x^{3} + 0.004 \cdot - 1815750 = 0$

Step 3.2.3

Factor $0.004$ out of $0.004 x^{3} + 0.004 \cdot - 1815750$ .

$0.004 (x^{3} - 1815750) = 0$

Step 3.3

Divide each term in $0.004 (x^{3} - 1815750) = 0$ by $0.004$ and simplify.

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Step 3.3.1

Divide each term in $0.004 (x^{3} - 1815750) = 0$ by $0.004$ .

$\frac{0.004 (x^{3} - 1815750)}{0.004} = \frac{0}{0.004}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $0.004$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{0.004 (x^{3} - 1815750)}{0.004} = \frac{0}{0.004}$

Step 3.3.2.1.2

Divide $x^{3} - 1815750$ by $1$ .

$x^{3} - 1815750 = \frac{0}{0.004}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $0$ by $0.004$ .

$x^{3} - 1815750 = 0$

Step 3.4

Add $1815750$ to both sides of the equation.

$x^{3} = 1815750$

Step 3.5

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

$x = \sqrt[3]{1815750}$

Step 3.6

Simplify $\sqrt[3]{1815750}$ .

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Step 3.6.1

Rewrite $1815750$ as $15^{3} \cdot 538$ .

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Step 3.6.1.1

Factor $3375$ out of $1815750$ .

$x = \sqrt[3]{3375 (538)}$

Step 3.6.1.2

Rewrite $3375$ as $15^{3}$ .

$x = \sqrt[3]{15^{3} \cdot 538}$

Step 3.6.2

Pull terms out from under the radical.

$x = 15 \sqrt[3]{538}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 15 \sqrt[3]{538}$

Decimal Form:

$x = 121.99780521 \dots$