Basic Math Examples

5^{2 n + 1} = 5^{2 n + 2} - (100)

$5^{2 n + 1} = 5^{2 n + 2} - (100)$

Step 1

Factor out

5^{2 n + 1}

$5^{2 n + 1}$ from the expression.

5^{2 n + 1} (1 - 5)

$5^{2 n + 1} (1 - 5)$

Step 2

Subtract

5^{2 n + 2}

$5^{2 n + 2}$ from both sides of the equation.

5^{2 n + 1} - 5^{2 n + 2} = - (100)

$5^{2 n + 1} - 5^{2 n + 2} = - (100)$

Step 3

Subtract

5

$5$ from

1

$1$ .

5^{2 n + 1} \cdot - 4 = - (100)

$5^{2 n + 1} \cdot - 4 = - (100)$

Step 4

Move

- 4

$- 4$ to the left of

5^{2 n + 1}

$5^{2 n + 1}$ .

- 4 \cdot 5^{2 n + 1} = - (100)

$- 4 \cdot 5^{2 n + 1} = - (100)$

Step 5

Multiply

- 1

$- 1$ by

100

$100$ .

- 4 \cdot 5^{2 n + 1} = - 100

$- 4 \cdot 5^{2 n + 1} = - 100$

Step 6

Divide each term in

- 4 \cdot 5^{2 n + 1} = - 100

$- 4 \cdot 5^{2 n + 1} = - 100$ by

- 4

$- 4$ and simplify.

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Step 6.1

Divide each term in

- 4 \cdot 5^{2 n + 1} = - 100

$- 4 \cdot 5^{2 n + 1} = - 100$ by

- 4

$- 4$ .

\frac{- 4 \cdot 5^{2 n + 1}}{- 4} = \frac{- 100}{- 4}

$\frac{- 4 \cdot 5^{2 n + 1}}{- 4} = \frac{- 100}{- 4}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

- 4

$- 4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 4 \cdot 5^{2 n + 1}}{- 4} = \frac{- 100}{- 4}$

Step 6.2.1.2

Divide

$5^{2 n + 1}$ by

$1$ .

$5^{2 n + 1} = \frac{- 100}{- 4}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide

$- 100$ by

$- 4$ .

$5^{2 n + 1} = 25$

Step 7

Create equivalent expressions in the equation that all have equal bases.

$5^{2 n + 1} = 5^{2}$

Step 8

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 n + 1 = 2$

Step 9

Solve for

$n$ .

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Step 9.1

Move all terms not containing

$n$ to the right side of the equation.

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Step 9.1.1

Subtract

$1$ from both sides of the equation.

$2 n = 2 - 1$

Step 9.1.2

Subtract

$1$ from

$2$ .

$2 n = 1$

Step 9.2

Divide each term in

$2 n = 1$ by

$2$ and simplify.

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Step 9.2.1

Divide each term in

$2 n = 1$ by

$2$ .

$\frac{2 n}{2} = \frac{1}{2}$

Step 9.2.2

Simplify the left side.

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Step 9.2.2.1

Cancel the common factor of

$2$ .

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Step 9.2.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{1}{2}$

Step 9.2.2.1.2

Divide

$n$ by

$1$ .

$n = \frac{1}{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{2}$

Decimal Form:

$n = 0.5$