Solve by Factoring x^3+9x=0

$x^{3} + 9 x = 0$

Step 1

Factor $x$ out of $x^{3} + 9 x$ .

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

$x \cdot x^{2} + 9 x = 0$

Factor $x$ out of $9 x$ .

$x \cdot x^{2} + x \cdot 9 = 0$

Factor $x$ out of $x \cdot x^{2} + x \cdot 9$ .

$x (x^{2} + 9) = 0$

Step 2

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

$x = 0$

$x^{2} + 9 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $x^{2} + 9$ equal to $0$ and solve for $x$ .

Set $x^{2} + 9$ equal to $0$ .

$x^{2} + 9 = 0$

Solve $x^{2} + 9 = 0$ for $x$ .

Subtract $9$ from both sides of the equation.

$x^{2} = - 9$

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

$x = \pm \sqrt{- 9}$

Simplify $\pm \sqrt{- 9}$ .

Rewrite $- 9$ as $- 1 (9)$ .

$x = \pm \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{9}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{9}$

Rewrite $9$ as $3^{2}$ .

$x = \pm i \cdot \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm i \cdot 3$

Move $3$ to the left of $i$ .

$x = \pm 3 i$

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.

$x = 3 i$

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

$x = - 3 i$

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

$x = 3 i, - 3 i$

Step 5

The final solution is all the values that make $x (x^{2} + 9) = 0$ true.

$x = 0, 3 i, - 3 i$

Solve by Factoring x^3+9x=0

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