Calculus Examples

$1 - \frac{1}{95} x^{2} = 0$

Step 1

Combine $x^{2}$ and $\frac{1}{95}$ .

$1 - \frac{x^{2}}{95} = 0$

Step 2

Subtract $1$ from both sides of the equation.

$- \frac{x^{2}}{95} = - 1$

Step 3

Multiply both sides of the equation by $- 95$ .

$- 95 (- \frac{x^{2}}{95}) = - 95 \cdot - 1$

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 $- 95 (- \frac{x^{2}}{95})$ .

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Step 4.1.1.1

Cancel the common factor of $95$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x^{2}}{95}$ into the numerator.

$- 95 \frac{- x^{2}}{95} = - 95 \cdot - 1$

Step 4.1.1.1.2

Factor $95$ out of $- 95$ .

$95 (- 1) \frac{- x^{2}}{95} = - 95 \cdot - 1$

Step 4.1.1.1.3

Cancel the common factor.

$95 \cdot - 1 \frac{- x^{2}}{95} = - 95 \cdot - 1$

Step 4.1.1.1.4

Rewrite the expression.

$- - x^{2} = - 95 \cdot - 1$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 95 \cdot - 1$

Step 4.1.1.2.2

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

$x^{2} = - 95 \cdot - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 95$ by $- 1$ .

$x^{2} = 95$

Step 5

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

$x = \pm \sqrt{95}$

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.

$x = \sqrt{95}$

Step 6.2

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

$x = - \sqrt{95}$

Step 6.3

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

$x = \sqrt{95}, - \sqrt{95}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{95}, - \sqrt{95}$

Decimal Form:

$x = 9.74679434 \dots, - 9.74679434 \dots$