Calculus Examples

$1 - \frac{49}{x^{2}} = 0$

Step 1

Subtract $1$ from both sides of the equation.

$- \frac{49}{x^{2}} = - 1$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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 2.2

The LCM of one and any expression is the expression.

$x^{2}$

Step 3

Multiply each term in $- \frac{49}{x^{2}} = - 1$ by $x^{2}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{49}{x^{2}} = - 1$ by $x^{2}$ .

$- \frac{49}{x^{2}} x^{2} = - x^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Move the leading negative in $- \frac{49}{x^{2}}$ into the numerator.

$\frac{- 49}{x^{2}} x^{2} = - x^{2}$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 49}{x^{2}} x^{2} = - x^{2}$

Step 3.2.1.3

Rewrite the expression.

$- 49 = - x^{2}$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $- x^{2} = - 49$ .

$- x^{2} = - 49$

Step 4.2

Divide each term in $- x^{2} = - 49$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x^{2} = - 49$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 49}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 49}{- 1}$

Step 4.2.2.2

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

$x^{2} = \frac{- 49}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 49$ by $- 1$ .

$x^{2} = 49$

Step 4.3

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

$x = \pm \sqrt{49}$

Step 4.4

Simplify $\pm \sqrt{49}$ .

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Step 4.4.1

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

Step 4.4.2

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

$x = \pm 7$

Step 4.5

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

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Step 4.5.1

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

$x = 7$

Step 4.5.2

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

$x = - 7$

Step 4.5.3

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

$x = 7, - 7$