Solve for x x^5-5x^2=0

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

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

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

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

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

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

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

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

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

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

$x = \pm \sqrt{0}$

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

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Simplify the right side of the equation.

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

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

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

$x = \pm 0$

$\pm 0$ is equal to $0$ .

$x = 0$

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

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Set the factor equal to $0$ .

$x^{3} - 5 = 0$

Add $5$ to both sides of the equation.

$x^{3} = 5$

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

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

The solution is the result of $x^{2} = 0$ and $x^{3} - 5 = 0$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0, 1.70997594 \dots$

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