Calculus Examples

$1 - \frac{1}{65} x^{2} = 0$

Step 1

Combine $x^{2}$ and $\frac{1}{65}$ .

$1 - \frac{x^{2}}{65} = 0$

Step 2

Subtract $1$ from both sides of the equation.

$- \frac{x^{2}}{65} = - 1$

Step 3

Multiply both sides of the equation by $- 65$ .

$- 65 (- \frac{x^{2}}{65}) = - 65 \cdot - 1$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 65 (- \frac{x^{2}}{65})$ .

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Step 4.1.1.1

Cancel the common factor of $65$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x^{2}}{65}$ into the numerator.

$- 65 \frac{- x^{2}}{65} = - 65 \cdot - 1$

Step 4.1.1.1.2

Factor $65$ out of $- 65$ .

$65 (- 1) \frac{- x^{2}}{65} = - 65 \cdot - 1$

Step 4.1.1.1.3

Cancel the common factor.

$65 \cdot - 1 \frac{- x^{2}}{65} = - 65 \cdot - 1$

Step 4.1.1.1.4

Rewrite the expression.

$- - x^{2} = - 65 \cdot - 1$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 65 \cdot - 1$

Step 4.1.1.2.2

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

$x^{2} = - 65 \cdot - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 65$ by $- 1$ .

$x^{2} = 65$

Step 5

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

$x = \pm \sqrt{65}$

Step 6

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

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Step 6.1

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

$x = \sqrt{65}$

Step 6.2

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

$x = - \sqrt{65}$

Step 6.3

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

$x = \sqrt{65}, - \sqrt{65}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{65}, - \sqrt{65}$

Decimal Form:

$x = 8.06225774 \dots, - 8.06225774 \dots$