Algebra Examples

$x^{2} (x - 100) (x - 200)$

Step 1

Set $x^{2} (x - 100) (x - 200)$ equal to $0$ .

$x^{2} (x - 100) (x - 200) = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

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

$x^{2} = 0$

$x - 100 = 0$

$x - 200 = 0$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$x^{2} = 0$

Step 2.2.2

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

Tap for more steps...

Step 2.2.2.1

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

$x = \pm \sqrt{0}$

Step 2.2.2.2

Simplify $\pm \sqrt{0}$ .

Tap for more steps...

Step 2.2.2.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 2.2.2.2.2

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

$x = \pm 0$

Step 2.2.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 2.3

Set $x - 100$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set $x - 100$ equal to $0$ .

$x - 100 = 0$

Step 2.3.2

Add $100$ to both sides of the equation.

$x = 100$

Step 2.4

Set $x - 200$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $x - 200$ equal to $0$ .

$x - 200 = 0$

Step 2.4.2

Add $200$ to both sides of the equation.

$x = 200$

Step 2.5

The final solution is all the values that make $x^{2} (x - 100) (x - 200) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 0$ (Multiplicity of $2$ )

$x = 100$ (Multiplicity of $1$ )

$x = 200$ (Multiplicity of $1$ )

$x = 0$ (Multiplicity of $2$ )

$x = 100$ (Multiplicity of $1$ )

$x = 200$ (Multiplicity of $1$ )

Step 3