Solve by Factoring 5x^3=50x

$5 x^{3} = 50 x$

Step 1

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

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

Step 2

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

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

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

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

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

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

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

Step 3

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

$x = 0$

$x^{2} - 10 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

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

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

$x^{2} - 10 = 0$

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

Add $10$ to both sides of the equation.

$x^{2} = 10$

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

$x = \pm \sqrt{10}$

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

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

$x = \sqrt{10}$

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

$x = - \sqrt{10}$

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

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

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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