Calculus Examples

$0 = - 30 x^{\frac{1}{2}} + 9$

Step 1

Rewrite the equation as $- 30 x^{\frac{1}{2}} + 9 = 0$ .

$- 30 x^{\frac{1}{2}} + 9 = 0$

Step 2

Subtract $9$ from both sides of the equation.

$- 30 x^{\frac{1}{2}} = - 9$

Step 3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(- 30 x^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${(- 30 x^{\frac{1}{2}})}^{2}$ .

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Step 4.1.1.1

Apply the product rule to $- 30 x^{\frac{1}{2}}$ .

${(- 30)}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Step 4.1.1.2

Raise $- 30$ to the power of $2$ .

$900 {(x^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Step 4.1.1.3

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 4.1.1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$900 x^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Step 4.1.1.3.2

Cancel the common factor of $2$ .

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Step 4.1.1.3.2.1

Cancel the common factor.

$900 x^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Step 4.1.1.3.2.2

Rewrite the expression.

$900 x^{1} = {(- 9)}^{2}$

Step 4.1.1.4

Simplify.

$900 x = {(- 9)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Raise $- 9$ to the power of $2$ .

$900 x = 81$

Step 5

Divide each term in $900 x = 81$ by $900$ and simplify.

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Step 5.1

Divide each term in $900 x = 81$ by $900$ .

$\frac{900 x}{900} = \frac{81}{900}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $900$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{900 x}{900} = \frac{81}{900}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{81}{900}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $81$ and $900$ .

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Step 5.3.1.1

Factor $9$ out of $81$ .

$x = \frac{9 (9)}{900}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $9$ out of $900$ .

$x = \frac{9 \cdot 9}{9 \cdot 100}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{9 \cdot 9}{9 \cdot 100}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{9}{100}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{100}$

Decimal Form:

$x = 0.09$