Basic Math Examples

$2 m^{2 + 14} = 11 m$

Step 1

Simplify $2 m^{2 + 14}$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 m^{2 + 14} = 11 m$

Step 1.2

Simplify by adding zeros.

$2 m^{2 + 14} = 11 m$

Step 1.3

Add $2$ and $14$ .

$2 m^{16} = 11 m$

Step 2

Subtract $11 m$ from both sides of the equation.

$2 m^{16} - 11 m = 0$

Step 3

Factor $m$ out of $2 m^{16} - 11 m$ .

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Step 3.1

Factor $m$ out of $2 m^{16}$ .

$m (2 m^{15}) - 11 m = 0$

Step 3.2

Factor $m$ out of $- 11 m$ .

$m (2 m^{15}) + m \cdot - 11 = 0$

Step 3.3

Factor $m$ out of $m (2 m^{15}) + m \cdot - 11$ .

$m (2 m^{15} - 11) = 0$

Step 4

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

$m = 0$

$2 m^{15} - 11 = 0$

Step 5

Set $m$ equal to $0$ .

$m = 0$

Step 6

Set $2 m^{15} - 11$ equal to $0$ and solve for $m$ .

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Step 6.1

Set $2 m^{15} - 11$ equal to $0$ .

$2 m^{15} - 11 = 0$

Step 6.2

Solve $2 m^{15} - 11 = 0$ for $m$ .

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Step 6.2.1

Add $11$ to both sides of the equation.

$2 m^{15} = 11$

Step 6.2.2

Divide each term in $2 m^{15} = 11$ by $2$ and simplify.

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Step 6.2.2.1

Divide each term in $2 m^{15} = 11$ by $2$ .

$\frac{2 m^{15}}{2} = \frac{11}{2}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $2$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{2 m^{15}}{2} = \frac{11}{2}$

Step 6.2.2.2.1.2

Divide $m^{15}$ by $1$ .

$m^{15} = \frac{11}{2}$

Step 6.2.3

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

$m = \sqrt[15]{\frac{11}{2}}$

Step 6.2.4

Rewrite $\sqrt[15]{\frac{11}{2}}$ as $\frac{\sqrt[15]{11}}{\sqrt[15]{2}}$ .

$m = \frac{\sqrt[15]{11}}{\sqrt[15]{2}}$

Step 7

The final solution is all the values that make $m (2 m^{15} - 11) = 0$ true.

$m = 0, \frac{\sqrt[15]{11}}{\sqrt[15]{2}}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$m = 0, \frac{\sqrt[15]{11}}{\sqrt[15]{2}}$

Decimal Form:

$m = 0, 1.12035978 \dots$