Finite Math Examples

$\frac{x^{2}}{3.4 \cdot 10^{- 3}} = 1.4 \cdot 10^{- 4}$

Step 1

Multiply both sides of the equation by $3.4 \cdot 10^{- 3}$ .

$3.4 \cdot 10^{- 3} \frac{x^{2}}{3.4 \cdot 10^{- 3}} = 3.4 \cdot 10^{- 3} \cdot 1.4 \cdot 10^{- 4}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3.4 \cdot 10^{- 3}$ .

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Step 2.1.1.1

Cancel the common factor.

$3.4 \cdot 10^{- 3} \frac{x^{2}}{3.4 \cdot 10^{- 3}} = 3.4 \cdot 10^{- 3} \cdot 1.4 \cdot 10^{- 4}$

Step 2.1.1.2

Rewrite the expression.

$x^{2} = 3.4 \cdot 10^{- 3} \cdot 1.4 \cdot 10^{- 4}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $3.4 \cdot 10^{- 3} \cdot 1.4 \cdot 10^{- 4}$ .

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Step 2.2.1.1

Multiply $3.4$ by $1.4$ .

$x^{2} = 4.76 (10^{- 3} \cdot 10^{- 4})$

Step 2.2.1.2

Multiply $10^{- 3}$ by $10^{- 4}$ by adding the exponents.

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Step 2.2.1.2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} = 4.76 \cdot 10^{- 3 - 4}$

Step 2.2.1.2.2

Subtract $4$ from $- 3$ .

$x^{2} = 4.76 \cdot 10^{- 7}$

Step 3

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

$x = \pm \sqrt{4.76 \cdot 10^{- 7}}$

Step 4

Simplify $\pm \sqrt{4.76 \cdot 10^{- 7}}$ .

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Step 4.1

Rewrite $4.76 \cdot 10^{- 7}$ as $0.476 \cdot 10^{- 6}$ .

$x = \pm \sqrt{0.476 \cdot 10^{- 6}}$

Step 4.2

Rewrite $\sqrt{0.476 \cdot 10^{- 6}}$ as $\sqrt{0.476} \cdot \sqrt{10^{- 6}}$ .

$x = \pm \sqrt{0.476} \cdot \sqrt{10^{- 6}}$

Step 4.3

Evaluate the root.

$x = \pm 0.68992753 \cdot \sqrt{10^{- 6}}$

Step 4.4

Rewrite $10^{- 6}$ as ${(10^{- 3})}^{2}$ .

$x = \pm 0.68992753 \cdot \sqrt{{(10^{- 3})}^{2}}$

Step 4.5

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

$x = \pm 0.68992753 \cdot 10^{- 3}$

Step 4.6

Move the decimal point in $0.68992753$ to the right by $1$ place and decrease the power of $10^{- 3}$ by $1$ .

$x = \pm 6.89927532 \cdot 10^{- 4}$

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.

$x = 6.89927532 \cdot 10^{- 4}$

Step 5.2

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

$x = - 6.89927532 \cdot 10^{- 4}$

Step 5.3

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

$x = 6.89927532 \cdot 10^{- 4}, - 6.89927532 \cdot 10^{- 4}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$x = 6.89927532 \cdot 10^{- 4}, - 6.89927532 \cdot 10^{- 4}$

Expanded Form:

$x = 0.00068992, - 0.00068992$