Precalculus Examples

x^{5} - 6 x^{2} = 0

$x^{5} - 6 x^{2} = 0$

Step 1

Factor

x^{2}

$x^{2}$ out of

x^{5} - 6 x^{2}

$x^{5} - 6 x^{2}$ .

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Step 1.1

Factor

x^{2}

$x^{2}$ out of

x^{5}

$x^{5}$ .

x^{2} x^{3} - 6 x^{2} = 0

$x^{2} x^{3} - 6 x^{2} = 0$

Step 1.2

Factor

x^{2}

$x^{2}$ out of

- 6 x^{2}

$- 6 x^{2}$ .

x^{2} x^{3} + x^{2} \cdot - 6 = 0

$x^{2} x^{3} + x^{2} \cdot - 6 = 0$

Step 1.3

Factor

x^{2}

$x^{2}$ out of

x^{2} x^{3} + x^{2} \cdot - 6

$x^{2} x^{3} + x^{2} \cdot - 6$ .

x^{2} (x^{3} - 6) = 0

$x^{2} (x^{3} - 6) = 0$

x^{2} (x^{3} - 6) = 0

$x^{2} (x^{3} - 6) = 0$

Step 2

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x^{2} = 0

$x^{2} = 0$

x^{3} - 6 = 0

$x^{3} - 6 = 0$

Step 3

Set

x^{2}

$x^{2}$ equal to

0

$0$ and solve for

x

$x$ .

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Step 3.1

Set

x^{2}

$x^{2}$ equal to

0

$0$ .

x^{2} = 0

$x^{2} = 0$

Step 3.2

Solve

x^{2} = 0

$x^{2} = 0$ for

x

$x$ .

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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}

$x = \pm \sqrt{0}$

Step 3.2.2

Simplify

\pm \sqrt{0}

$\pm \sqrt{0}$ .

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Step 3.2.2.1

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

x = \pm \sqrt{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

$x = \pm 0$

Step 3.2.2.3

Plus or minus

0

$0$ is

0

$0$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

Step 4

Set

x^{3} - 6

$x^{3} - 6$ equal to

0

$0$ and solve for

x

$x$ .

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Step 4.1

Set

x^{3} - 6

$x^{3} - 6$ equal to

0

$0$ .

x^{3} - 6 = 0

$x^{3} - 6 = 0$

Step 4.2

Solve

x^{3} - 6 = 0

$x^{3} - 6 = 0$ for

x

$x$ .

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Step 4.2.1

Add

6

$6$ to both sides of the equation.

x^{3} = 6

$x^{3} = 6$

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]{6}

$x = \sqrt[3]{6}$

x = \sqrt[3]{6}

$x = \sqrt[3]{6}$

x = \sqrt[3]{6}

$x = \sqrt[3]{6}$

Step 5

The final solution is all the values that make

x^{2} (x^{3} - 6) = 0

$x^{2} (x^{3} - 6) = 0$ true.

x = 0, \sqrt[3]{6}

$x = 0, \sqrt[3]{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

x = 0, \sqrt[3]{6}

$x = 0, \sqrt[3]{6}$

Decimal Form:

x = 0, 1.81712059 \dots

$x = 0, 1.81712059 \dots$