Finite Math Examples

$2 - 40000 x^{- 2} = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 - 40000 \frac{1}{x^{2}} = 0$

Step 1.2

Combine $- 40000$ and $\frac{1}{x^{2}}$ .

$2 + \frac{- 40000}{x^{2}} = 0$

Step 1.3

Move the negative in front of the fraction.

$2 - \frac{40000}{x^{2}} = 0$

Step 2

Subtract $2$ from both sides of the equation.

$- \frac{40000}{x^{2}} = - 2$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x^{2}, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x^{2}$

Step 4

Multiply each term in $- \frac{40000}{x^{2}} = - 2$ by $x^{2}$ to eliminate the fractions.

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Step 4.1

Multiply each term in $- \frac{40000}{x^{2}} = - 2$ by $x^{2}$ .

$- \frac{40000}{x^{2}} x^{2} = - 2 x^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x^{2}$ .

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Step 4.2.1.1

Move the leading negative in $- \frac{40000}{x^{2}}$ into the numerator.

$\frac{- 40000}{x^{2}} x^{2} = - 2 x^{2}$

Step 4.2.1.2

Cancel the common factor.

$\frac{- 40000}{x^{2}} x^{2} = - 2 x^{2}$

Step 4.2.1.3

Rewrite the expression.

$- 40000 = - 2 x^{2}$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $- 2 x^{2} = - 40000$ .

$- 2 x^{2} = - 40000$

Step 5.2

Divide each term in $- 2 x^{2} = - 40000$ by $- 2$ and simplify.

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Step 5.2.1

Divide each term in $- 2 x^{2} = - 40000$ by $- 2$ .

$\frac{- 2 x^{2}}{- 2} = \frac{- 40000}{- 2}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 2 x^{2}}{- 2} = \frac{- 40000}{- 2}$

Step 5.2.2.1.2

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

$x^{2} = \frac{- 40000}{- 2}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 40000$ by $- 2$ .

$x^{2} = 20000$

Step 5.3

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

$x = \pm \sqrt{20000}$

Step 5.4

Simplify $\pm \sqrt{20000}$ .

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Step 5.4.1

Rewrite $20000$ as $100^{2} \cdot 2$ .

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Step 5.4.1.1

Factor $10000$ out of $20000$ .

$x = \pm \sqrt{10000 (2)}$

Step 5.4.1.2

Rewrite $10000$ as $100^{2}$ .

$x = \pm \sqrt{100^{2} \cdot 2}$

Step 5.4.2

Pull terms out from under the radical.

$x = \pm 100 \sqrt{2}$

Step 5.5

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

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Step 5.5.1

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

$x = 100 \sqrt{2}$

Step 5.5.2

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

$x = - 100 \sqrt{2}$

Step 5.5.3

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

$x = 100 \sqrt{2}, - 100 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 100 \sqrt{2}, - 100 \sqrt{2}$

Decimal Form:

$x = 141.42135623 \dots, - 141.42135623 \dots$