Finite Math Examples

f (x) = \frac{20 \sqrt{x}}{{(x \sqrt{x} + 5)}^{2}}

$f (x) = \frac{20 \sqrt{x}}{{(x \sqrt{x} + 5)}^{2}}$

Step 1

Set

\frac{20 \sqrt{x}}{{(x \sqrt{x} + 5)}^{2}}

$\frac{20 \sqrt{x}}{{(x \sqrt{x} + 5)}^{2}}$ equal to

0

$0$ .

\frac{20 \sqrt{x}}{{(x \sqrt{x} + 5)}^{2}} = 0

$\frac{20 \sqrt{x}}{{(x \sqrt{x} + 5)}^{2}} = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Set the numerator equal to zero.

20 \sqrt{x} = 0

$20 \sqrt{x} = 0$

Step 2.2

Solve the equation for

x

$x$ .

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Step 2.2.1

To remove the radical on the left side of the equation, square both sides of the equation.

{(20 \sqrt{x})}^{2} = 0^{2}

${(20 \sqrt{x})}^{2} = 0^{2}$

Step 2.2.2

Simplify each side of the equation.

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Step 2.2.2.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{x}

$\sqrt{x}$ as

x^{\frac{1}{2}}

$x^{\frac{1}{2}}$ .

{(20 x^{\frac{1}{2}})}^{2} = 0^{2}

${(20 x^{\frac{1}{2}})}^{2} = 0^{2}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Simplify

{(20 x^{\frac{1}{2}})}^{2}

${(20 x^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.2.1.1

Apply the product rule to

20 x^{\frac{1}{2}}

$20 x^{\frac{1}{2}}$ .

20^{2} {(x^{\frac{1}{2}})}^{2} = 0^{2}

$20^{2} {(x^{\frac{1}{2}})}^{2} = 0^{2}$

Step 2.2.2.2.1.2

Raise

20

$20$ to the power of

2

$2$ .

400 {(x^{\frac{1}{2}})}^{2} = 0^{2}

$400 {(x^{\frac{1}{2}})}^{2} = 0^{2}$

Step 2.2.2.2.1.3

Multiply the exponents in

{(x^{\frac{1}{2}})}^{2}

${(x^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.2.1.3.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

400 x^{\frac{1}{2} \cdot 2} = 0^{2}

$400 x^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 2.2.2.2.1.3.2

Cancel the common factor of

2

$2$ .

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Step 2.2.2.2.1.3.2.1

Cancel the common factor.

400 x^{\frac{1}{2} \cdot 2} = 0^{2}

$400 x^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 2.2.2.2.1.3.2.2

Rewrite the expression.

400 x^{1} = 0^{2}

$400 x^{1} = 0^{2}$

400 x^{1} = 0^{2}

$400 x^{1} = 0^{2}$

400 x^{1} = 0^{2}

$400 x^{1} = 0^{2}$

Step 2.2.2.2.1.4

Simplify.

400 x = 0^{2}

$400 x = 0^{2}$

400 x = 0^{2}

$400 x = 0^{2}$

400 x = 0^{2}

$400 x = 0^{2}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Raising

0

$0$ to any positive power yields

0

$0$ .

400 x = 0

$400 x = 0$

400 x = 0

$400 x = 0$

400 x = 0

$400 x = 0$

Step 2.2.3

Divide each term in

400 x = 0

$400 x = 0$ by

400

$400$ and simplify.

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Step 2.2.3.1

Divide each term in

400 x = 0

$400 x = 0$ by

400

$400$ .

\frac{400 x}{400} = \frac{0}{400}

$\frac{400 x}{400} = \frac{0}{400}$

Step 2.2.3.2

Simplify the left side.

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Step 2.2.3.2.1

Cancel the common factor of

400

$400$ .

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Step 2.2.3.2.1.1

Cancel the common factor.

\frac{400 x}{400} = \frac{0}{400}

$\frac{400 x}{400} = \frac{0}{400}$

Step 2.2.3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{0}{400}

$x = \frac{0}{400}$

x = \frac{0}{400}

$x = \frac{0}{400}$

x = \frac{0}{400}

$x = \frac{0}{400}$

Step 2.2.3.3

Simplify the right side.

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Step 2.2.3.3.1

Divide

0

$0$ by

400

$400$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

Step 3

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$