Pre-Algebra Examples

$11.85 = \frac{x^{2}}{(0.25) \cdot {(0.1)}^{3}}$

Step 1

Rewrite the equation as $\frac{x^{2}}{0.25 \cdot {0.1}^{3}} = 11.85$ .

$\frac{x^{2}}{0.25 \cdot {0.1}^{3}} = 11.85$

Step 2

Multiply both sides of the equation by $0.25 \cdot {0.1}^{3}$ .

$0.25 \cdot {0.1}^{3} \frac{x^{2}}{0.25 \cdot {0.1}^{3}} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $0.25 \cdot {0.1}^{3} \frac{x^{2}}{0.25 \cdot {0.1}^{3}}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $0.00025$ .

Tap for more steps...

Step 3.1.1.1.1

Factor $0.00025$ out of $0.25 \cdot {0.1}^{3}$ .

$0.00025 (1000 \cdot {0.1}^{3}) \frac{x^{2}}{0.25 \cdot {0.1}^{3}} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.1.2

Factor $0.00025$ out of $0.25 \cdot {0.1}^{3}$ .

$0.00025 (1000 \cdot {0.1}^{3}) \frac{x^{2}}{0.00025 (1000 \cdot {0.1}^{3})} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.1.3

Cancel the common factor.

$0.00025 (1000 \cdot {0.1}^{3}) \frac{x^{2}}{0.00025 (1000 \cdot {0.1}^{3})} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.1.4

Rewrite the expression.

$1000 \cdot {0.1}^{3} \frac{x^{2}}{1000 \cdot {0.1}^{3}} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.2

Combine $1000$ and $\frac{x^{2}}{1000 \cdot {0.1}^{3}}$ .

${0.1}^{3} \frac{1000 x^{2}}{1000 \cdot {0.1}^{3}} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.3

Combine ${0.1}^{3}$ and $\frac{1000 x^{2}}{1000 \cdot {0.1}^{3}}$ .

$\frac{{0.1}^{3} (1000 x^{2})}{1000 \cdot {0.1}^{3}} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.4

Cancel the common factor of ${0.1}^{3}$ .

Tap for more steps...

Step 3.1.1.4.1

Cancel the common factor.

$\frac{{0.1}^{3} (1000 x^{2})}{1000 \cdot {0.1}^{3}} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.4.2

Rewrite the expression.

$\frac{1000 x^{2}}{1000} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.5

Cancel the common factor of $1000$ .

Tap for more steps...

Step 3.1.1.5.1

Cancel the common factor.

$\frac{1000 x^{2}}{1000} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.1.1.5.2

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

$x^{2} = 0.25 \cdot {0.1}^{3} \cdot 11.85$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $0.25 \cdot {0.1}^{3} \cdot 11.85$ .

Tap for more steps...

Step 3.2.1.1

Raise $0.1$ to the power of $3$ .

$x^{2} = 0.25 \cdot 0.001 \cdot 11.85$

Step 3.2.1.2

Multiply $0.25 \cdot 0.001 \cdot 11.85$ .

Tap for more steps...

Step 3.2.1.2.1

Multiply $0.25$ by $0.001$ .

$x^{2} = 0.00025 \cdot 11.85$

Step 3.2.1.2.2

Multiply $0.00025$ by $11.85$ .

$x^{2} = 0.0029625$

Step 4

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

$x = \pm \sqrt{0.0029625}$

Step 5

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

Tap for more steps...

Step 5.1

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

$x = \sqrt{0.0029625}$

Step 5.2

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

$x = - \sqrt{0.0029625}$

Step 5.3

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

$x = \sqrt{0.0029625}, - \sqrt{0.0029625}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{0.0029625}, - \sqrt{0.0029625}$

Decimal Form:

$x = 0.05442885 \dots, - 0.05442885 \dots$