Solve for x x^3=3x

$x^{3} = 3 x$

Step 1

Subtract $3 x$ from both sides of the equation.

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

Step 2

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

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

$x \cdot x^{2} - 3 x = 0$

Factor $x$ out of $- 3 x$ .

$x \cdot x^{2} + x \cdot - 3 = 0$

Factor $x$ out of $x \cdot x^{2} + x \cdot - 3$ .

$x (x^{2} - 3) = 0$

Step 3

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

$x = 0$

$x^{2} - 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x^{2} - 3$ equal to $0$ and solve for $x$ .

Set $x^{2} - 3$ equal to $0$ .

$x^{2} - 3 = 0$

Solve $x^{2} - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$x^{2} = 3$

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

$x = \pm \sqrt{3}$

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.

$x = \sqrt{3}$

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

$x = - \sqrt{3}$

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

$x = \sqrt{3}, - \sqrt{3}$

Step 6

The final solution is all the values that make $x (x^{2} - 3) = 0$ true.

$x = 0, \sqrt{3}, - \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, \sqrt{3}, - \sqrt{3}$

Decimal Form:

$x = 0, 1.73205080 \dots, - 1.73205080 \dots$