Calculus Examples

$0 = x - \frac{1}{70} x^{3}$

Step 1

Rewrite the equation as $x - \frac{1}{70} x^{3} = 0$ .

$x - \frac{1}{70} x^{3} = 0$

Step 2

Combine $x^{3}$ and $\frac{1}{70}$ .

$x - \frac{x^{3}}{70} = 0$

Step 3

Factor $x$ out of $x - \frac{x^{3}}{70}$ .

Tap for more steps...

Step 3.1

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - \frac{x^{3}}{70} = 0$

Step 3.2

Factor $x$ out of $- \frac{x^{3}}{70}$ .

$x \cdot 1 + x (- \frac{x^{2}}{70}) = 0$

Step 3.3

Factor $x$ out of $x \cdot 1 + x (- \frac{x^{2}}{70})$ .

$x (1 - \frac{x^{2}}{70}) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$1 - \frac{x^{2}}{70} = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $1 - \frac{x^{2}}{70}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 6.1

Set $1 - \frac{x^{2}}{70}$ equal to $0$ .

$1 - \frac{x^{2}}{70} = 0$

Step 6.2

Solve $1 - \frac{x^{2}}{70} = 0$ for $x$ .

Tap for more steps...

Step 6.2.1

Subtract $1$ from both sides of the equation.

$- \frac{x^{2}}{70} = - 1$

Step 6.2.2

Multiply both sides of the equation by $- 70$ .

$- 70 (- \frac{x^{2}}{70}) = - 70 \cdot - 1$

Step 6.2.3

Simplify both sides of the equation.

Tap for more steps...

Step 6.2.3.1

Simplify the left side.

Tap for more steps...

Step 6.2.3.1.1

Simplify $- 70 (- \frac{x^{2}}{70})$ .

Tap for more steps...

Step 6.2.3.1.1.1

Cancel the common factor of $70$ .

Tap for more steps...

Step 6.2.3.1.1.1.1

Move the leading negative in $- \frac{x^{2}}{70}$ into the numerator.

$- 70 \frac{- x^{2}}{70} = - 70 \cdot - 1$

Step 6.2.3.1.1.1.2

Factor $70$ out of $- 70$ .

$70 (- 1) \frac{- x^{2}}{70} = - 70 \cdot - 1$

Step 6.2.3.1.1.1.3

Cancel the common factor.

$70 \cdot - 1 \frac{- x^{2}}{70} = - 70 \cdot - 1$

Step 6.2.3.1.1.1.4

Rewrite the expression.

$- - x^{2} = - 70 \cdot - 1$

Step 6.2.3.1.1.2

Multiply.

Tap for more steps...

Step 6.2.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 70 \cdot - 1$

Step 6.2.3.1.1.2.2

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

$x^{2} = - 70 \cdot - 1$

Step 6.2.3.2

Simplify the right side.

Tap for more steps...

Step 6.2.3.2.1

Multiply $- 70$ by $- 1$ .

$x^{2} = 70$

Step 6.2.4

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

$x = \pm \sqrt{70}$

Step 6.2.5

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

Tap for more steps...

Step 6.2.5.1

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

$x = \sqrt{70}$

Step 6.2.5.2

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

$x = - \sqrt{70}$

Step 6.2.5.3

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

$x = \sqrt{70}, - \sqrt{70}$

Step 7

The final solution is all the values that make $x (1 - \frac{x^{2}}{70}) = 0$ true.

$x = 0, \sqrt{70}, - \sqrt{70}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 0, \sqrt{70}, - \sqrt{70}$

Decimal Form:

$x = 0, 8.36660026 \dots, - 8.36660026 \dots$