Calculus Examples

$1 - \frac{1}{40} x^{2} = 0$

Step 1

Combine $x^{2}$ and $\frac{1}{40}$ .

$1 - \frac{x^{2}}{40} = 0$

Step 2

Subtract $1$ from both sides of the equation.

$- \frac{x^{2}}{40} = - 1$

Step 3

Multiply both sides of the equation by $- 40$ .

$- 40 (- \frac{x^{2}}{40}) = - 40 \cdot - 1$

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 $- 40 (- \frac{x^{2}}{40})$ .

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Step 4.1.1.1

Cancel the common factor of $40$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x^{2}}{40}$ into the numerator.

$- 40 \frac{- x^{2}}{40} = - 40 \cdot - 1$

Step 4.1.1.1.2

Factor $40$ out of $- 40$ .

$40 (- 1) \frac{- x^{2}}{40} = - 40 \cdot - 1$

Step 4.1.1.1.3

Cancel the common factor.

$40 \cdot - 1 \frac{- x^{2}}{40} = - 40 \cdot - 1$

Step 4.1.1.1.4

Rewrite the expression.

$- - x^{2} = - 40 \cdot - 1$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 40 \cdot - 1$

Step 4.1.1.2.2

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

$x^{2} = - 40 \cdot - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 40$ by $- 1$ .

$x^{2} = 40$

Step 5

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

$x = \pm \sqrt{40}$

Step 6

Simplify $\pm \sqrt{40}$ .

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Step 6.1

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 6.1.1

Factor $4$ out of $40$ .

$x = \pm \sqrt{4 (10)}$

Step 6.1.2

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

$x = \pm \sqrt{2^{2} \cdot 10}$

Step 6.2

Pull terms out from under the radical.

$x = \pm 2 \sqrt{10}$

Step 7

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

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Step 7.1

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

$x = 2 \sqrt{10}$

Step 7.2

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

$x = - 2 \sqrt{10}$

Step 7.3

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

$x = 2 \sqrt{10}, - 2 \sqrt{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{10}, - 2 \sqrt{10}$

Decimal Form:

$x = 6.32455532 \dots, - 6.32455532 \dots$