Pre-Algebra Examples

$11.85 = \frac{x^{2}}{(0.25) \cdot {(0.15)}^{3}}$

Step 1

Rewrite the equation as $\frac{x^{2}}{0.25 \cdot {0.15}^{3}} = 11.85$ .

$\frac{x^{2}}{0.25 \cdot {0.15}^{3}} = 11.85$

Step 2

Multiply both sides of the equation by $0.25 \cdot {0.15}^{3}$ .

$0.25 \cdot {0.15}^{3} \frac{x^{2}}{0.25 \cdot {0.15}^{3}} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $0.25 \cdot {0.15}^{3} \frac{x^{2}}{0.25 \cdot {0.15}^{3}}$ .

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Step 3.1.1.1

Cancel the common factor of $0.00084375$ .

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Step 3.1.1.1.1

Factor $0.00084375$ out of $0.25 \cdot {0.15}^{3}$ .

$0.00084375 (296.\overline{296} \cdot {0.15}^{3}) \frac{x^{2}}{0.25 \cdot {0.15}^{3}} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.1.2

Factor $0.00084375$ out of $0.25 \cdot {0.15}^{3}$ .

$0.00084375 (296.\overline{296} \cdot {0.15}^{3}) \frac{x^{2}}{0.00084375 (296.\overline{296} \cdot {0.15}^{3})} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.1.3

Cancel the common factor.

$0.00084375 (296.\overline{296} \cdot {0.15}^{3}) \frac{x^{2}}{0.00084375 (296.\overline{296} \cdot {0.15}^{3})} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.1.4

Rewrite the expression.

$296.\overline{296} \cdot {0.15}^{3} \frac{x^{2}}{296.\overline{296} \cdot {0.15}^{3}} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.2

Multiply $296.\overline{296}$ by ${0.15}^{3}$ .

$1 \frac{x^{2}}{296.\overline{296} \cdot {0.15}^{3}} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.3

Multiply $296.\overline{296}$ by ${0.15}^{3}$ .

$1 \frac{x^{2}}{1} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.4

Simplify.

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Step 3.1.1.4.1

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

$\frac{x^{2}}{1} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.1.1.4.2

Divide $x^{2}$ by $1$ .

$x^{2} = 0.25 \cdot {0.15}^{3} \cdot 11.85$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $0.25 \cdot {0.15}^{3} \cdot 11.85$ .

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Step 3.2.1.1

Raise $0.15$ to the power of $3$ .

$x^{2} = 0.25 \cdot 0.003375 \cdot 11.85$

Step 3.2.1.2

Multiply $0.25 \cdot 0.003375 \cdot 11.85$ .

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Step 3.2.1.2.1

Multiply $0.25$ by $0.003375$ .

$x^{2} = 0.00084375 \cdot 11.85$

Step 3.2.1.2.2

Multiply $0.00084375$ by $11.85$ .

$x^{2} = 0.00999843$

Step 4

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

$x = \pm \sqrt{0.00999843}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{0.00999843}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{0.00999843}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{0.00999843}, - \sqrt{0.00999843}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{0.00999843}, - \sqrt{0.00999843}$

Decimal Form:

$x = 0.09999218 \dots, - 0.09999218 \dots$