Finite Math Examples

$50000 p^{2} = 0.01 p^{7}$

Step 1

Subtract $0.01 p^{7}$ from both sides of the equation.

$50000 p^{2} - 0.01 p^{7} = 0$

Step 2

Factor $0.01 p^{2}$ out of $50000 p^{2} - 0.01 p^{7}$ .

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Step 2.1

Factor $0.01 p^{2}$ out of $50000 p^{2}$ .

$0.01 p^{2} (5000000) - 0.01 p^{7} = 0$

Step 2.2

Factor $0.01 p^{2}$ out of $- 0.01 p^{7}$ .

$0.01 p^{2} (5000000) + 0.01 p^{2} (- p^{5}) = 0$

Step 2.3

Factor $0.01 p^{2}$ out of $0.01 p^{2} (5000000) + 0.01 p^{2} (- p^{5})$ .

$0.01 p^{2} (5000000 - p^{5}) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$p^{2} = 0$

$5000000 - p^{5} = 0$

Step 4

Set $p^{2}$ equal to $0$ and solve for $p$ .

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Step 4.1

Set $p^{2}$ equal to $0$ .

$p^{2} = 0$

Step 4.2

Solve $p^{2} = 0$ for $p$ .

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Step 4.2.1

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

$p = \pm \sqrt{0}$

Step 4.2.2

Simplify $\pm \sqrt{0}$ .

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Step 4.2.2.1

Rewrite $0$ as $0^{2}$ .

$p = \pm \sqrt{0^{2}}$

Step 4.2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$p = \pm 0$

Step 4.2.2.3

Plus or minus $0$ is $0$ .

$p = 0$

Step 5

Set $5000000 - p^{5}$ equal to $0$ and solve for $p$ .

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Step 5.1

Set $5000000 - p^{5}$ equal to $0$ .

$5000000 - p^{5} = 0$

Step 5.2

Solve $5000000 - p^{5} = 0$ for $p$ .

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Step 5.2.1

Subtract $5000000$ from both sides of the equation.

$- p^{5} = - 5000000$

Step 5.2.2

Divide each term in $- p^{5} = - 5000000$ by $- 1$ and simplify.

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Step 5.2.2.1

Divide each term in $- p^{5} = - 5000000$ by $- 1$ .

$\frac{- p^{5}}{- 1} = \frac{- 5000000}{- 1}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{p^{5}}{1} = \frac{- 5000000}{- 1}$

Step 5.2.2.2.2

Divide $p^{5}$ by $1$ .

$p^{5} = \frac{- 5000000}{- 1}$

Step 5.2.2.3

Simplify the right side.

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Step 5.2.2.3.1

Divide $- 5000000$ by $- 1$ .

$p^{5} = 5000000$

Step 5.2.3

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

$p = \sqrt[5]{5000000}$

Step 5.2.4

Simplify $\sqrt[5]{5000000}$ .

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Step 5.2.4.1

Rewrite $5000000$ as $10^{5} \cdot 50$ .

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Step 5.2.4.1.1

Factor $100000$ out of $5000000$ .

$p = \sqrt[5]{100000 (50)}$

Step 5.2.4.1.2

Rewrite $100000$ as $10^{5}$ .

$p = \sqrt[5]{10^{5} \cdot 50}$

Step 5.2.4.2

Pull terms out from under the radical.

$p = 10 \sqrt[5]{50}$

Step 6

The final solution is all the values that make $0.01 p^{2} (5000000 - p^{5}) = 0$ true.

$p = 0, 10 \sqrt[5]{50}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$p = 0, 10 \sqrt[5]{50}$

Decimal Form:

$p = 0, 21.86724147 \dots$