Algebra Examples

$5 w^{3} = 50 w$

Step 1

Subtract $50 w$ from both sides of the equation.

$5 w^{3} - 50 w = 0$

Step 2

Factor $5 w$ out of $5 w^{3} - 50 w$ .

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Step 2.1

Factor $5 w$ out of $5 w^{3}$ .

$5 w (w^{2}) - 50 w = 0$

Step 2.2

Factor $5 w$ out of $- 50 w$ .

$5 w (w^{2}) + 5 w (- 10) = 0$

Step 2.3

Factor $5 w$ out of $5 w (w^{2}) + 5 w (- 10)$ .

$5 w (w^{2} - 10) = 0$

Step 3

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

$w = 0$

$w^{2} - 10 = 0$

Step 4

Set $w$ equal to $0$ .

$w = 0$

Step 5

Set $w^{2} - 10$ equal to $0$ and solve for $w$ .

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Step 5.1

Set $w^{2} - 10$ equal to $0$ .

$w^{2} - 10 = 0$

Step 5.2

Solve $w^{2} - 10 = 0$ for $w$ .

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Step 5.2.1

Add $10$ to both sides of the equation.

$w^{2} = 10$

Step 5.2.2

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

$w = \pm \sqrt{10}$

Step 5.2.3

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

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Step 5.2.3.1

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

$w = \sqrt{10}$

Step 5.2.3.2

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

$w = - \sqrt{10}$

Step 5.2.3.3

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

$w = \sqrt{10}, - \sqrt{10}$

Step 6

The final solution is all the values that make $5 w (w^{2} - 10) = 0$ true.

$w = 0, \sqrt{10}, - \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$w = 0, \sqrt{10}, - \sqrt{10}$

Decimal Form:

$w = 0, 3.16227766 \dots, - 3.16227766 \dots$