Precalculus Examples

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

Step 1

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

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Step 1.1

Factor $x^{2}$ out of $x^{5}$ .

$x^{2} x^{3} - 5 x^{2} = 0$

Step 1.2

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

$x^{2} x^{3} + x^{2} \cdot - 5 = 0$

Step 1.3

Factor $x^{2}$ out of $x^{2} x^{3} + x^{2} \cdot - 5$ .

$x^{2} (x^{3} - 5) = 0$

Step 2

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

$x^{2} = 0$

$x^{3} - 5 = 0$

Step 3

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

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Step 3.1

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

$x^{2} = 0$

Step 3.2

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

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Step 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 3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

$x = \pm 0$

Step 3.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 4

Set $x^{3} - 5$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x^{3} - 5$ equal to $0$ .

$x^{3} - 5 = 0$

Step 4.2

Solve $x^{3} - 5 = 0$ for $x$ .

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Step 4.2.1

Add $5$ to both sides of the equation.

$x^{3} = 5$

Step 4.2.2

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

$x = \sqrt[3]{5}$

Step 5

The final solution is all the values that make $x^{2} (x^{3} - 5) = 0$ true.

$x = 0, \sqrt[3]{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, \sqrt[3]{5}$

Decimal Form:

$x = 0, 1.70997594 \dots$