Calculus Examples

$0 = 12 - \frac{192}{x^{2}}$

Step 1

Rewrite the equation as $12 - \frac{192}{x^{2}} = 0$ .

$12 - \frac{192}{x^{2}} = 0$

Step 2

Subtract $12$ from both sides of the equation.

$- \frac{192}{x^{2}} = - 12$

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 $- \frac{192}{x^{2}} = - 12$ by $x^{2}$ to eliminate the fractions.

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Step 4.1

Multiply each term in $- \frac{192}{x^{2}} = - 12$ by $x^{2}$ .

$- \frac{192}{x^{2}} x^{2} = - 12 x^{2}$

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 $- \frac{192}{x^{2}}$ into the numerator.

$\frac{- 192}{x^{2}} x^{2} = - 12 x^{2}$

Step 4.2.1.2

Cancel the common factor.

$\frac{- 192}{x^{2}} x^{2} = - 12 x^{2}$

Step 4.2.1.3

Rewrite the expression.

$- 192 = - 12 x^{2}$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $- 12 x^{2} = - 192$ .

$- 12 x^{2} = - 192$

Step 5.2

Divide each term in $- 12 x^{2} = - 192$ by $- 12$ and simplify.

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Step 5.2.1

Divide each term in $- 12 x^{2} = - 192$ by $- 12$ .

$\frac{- 12 x^{2}}{- 12} = \frac{- 192}{- 12}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 12$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 12 x^{2}}{- 12} = \frac{- 192}{- 12}$

Step 5.2.2.1.2

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

$x^{2} = \frac{- 192}{- 12}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 192$ by $- 12$ .

$x^{2} = 16$

Step 5.3

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

$x = \pm \sqrt{16}$

Step 5.4

Simplify $\pm \sqrt{16}$ .

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Step 5.4.1

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

Step 5.4.2

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

$x = \pm 4$

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.

$x = 4$

Step 5.5.2

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

$x = - 4$

Step 5.5.3

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

$x = 4, - 4$