Solve for x x^3-5x=0

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

Step 1

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

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

$x \cdot x^{2} - 5 x = 0$

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

$x \cdot x^{2} + x \cdot - 5 = 0$

Factor $x$ out of $x \cdot x^{2} + x \cdot - 5$ .

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

Step 2

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

$x = 0$

$x^{2} - 5 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $x^{2} - 5$ equal to $0$ and solve for $x$ .

Set $x^{2} - 5$ equal to $0$ .

$x^{2} - 5 = 0$

Solve $x^{2} - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$x^{2} = 5$

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

$x = \pm \sqrt{5}$

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.

$x = \sqrt{5}$

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

$x = - \sqrt{5}$

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

$x = \sqrt{5}, - \sqrt{5}$

Step 5

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

$x = 0, \sqrt{5}, - \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 0, 2.23606797 \dots, - 2.23606797 \dots$