Finite Math Examples

$f (x) = 9 x^{3} - 9 x^{2}$

Step 1

Set $9 x^{3} - 9 x^{2}$ equal to $0$ .

$9 x^{3} - 9 x^{2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor $9 x^{2}$ out of $9 x^{3} - 9 x^{2}$ .

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Step 2.1.1

Factor $9 x^{2}$ out of $9 x^{3}$ .

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

Step 2.1.2

Factor $9 x^{2}$ out of $- 9 x^{2}$ .

$9 x^{2} (x) + 9 x^{2} (- 1) = 0$

Step 2.1.3

Factor $9 x^{2}$ out of $9 x^{2} (x) + 9 x^{2} (- 1)$ .

$9 x^{2} (x - 1) = 0$

Step 2.2

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

$x^{2} = 0$

$x - 1 = 0$

Step 2.3

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

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Step 2.3.1

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

$x^{2} = 0$

Step 2.3.2

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

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Step 2.3.2.1

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

$x = \pm \sqrt{0}$

Step 2.3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.3.2.2.1

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

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

Step 2.3.2.2.2

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

$x = \pm 0$

Step 2.3.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 2.4

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.4.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.5

The final solution is all the values that make $9 x^{2} (x - 1) = 0$ true.

$x = 0, 1$

Step 3