Calculus Examples

$0 = x^{7} - 7 x$

Step 1

Rewrite the equation as $x^{7} - 7 x = 0$ .

$x^{7} - 7 x = 0$

Step 2

Factor $x$ out of $x^{7} - 7 x$ .

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Step 2.1

Factor $x$ out of $x^{7}$ .

$x \cdot x^{6} - 7 x = 0$

Step 2.2

Factor $x$ out of $- 7 x$ .

$x \cdot x^{6} + x \cdot - 7 = 0$

Step 2.3

Factor $x$ out of $x \cdot x^{6} + x \cdot - 7$ .

$x (x^{6} - 7) = 0$

Step 3

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

$x = 0$

$x^{6} - 7 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x^{6} - 7$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x^{6} - 7$ equal to $0$ .

$x^{6} - 7 = 0$

Step 5.2

Solve $x^{6} - 7 = 0$ for $x$ .

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Step 5.2.1

Add $7$ to both sides of the equation.

$x^{6} = 7$

Step 5.2.2

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

$x = \pm \sqrt[6]{7}$

Step 5.2.3

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

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Step 5.2.3.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt[6]{7}$

Step 5.2.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt[6]{7}$

Step 5.2.3.3

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

$x = \sqrt[6]{7}, - \sqrt[6]{7}$

Step 6

The final solution is all the values that make $x (x^{6} - 7) = 0$ true.

$x = 0, \sqrt[6]{7}, - \sqrt[6]{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, \sqrt[6]{7}, - \sqrt[6]{7}$

Decimal Form:

$x = 0, 1.38308755 \dots, - 1.38308755 \dots$