Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Subtract $5$ from $1$ .

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

Step 4

Move $- 4$ to the left of $5^{2 n + 1}$ .

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

Step 5

Multiply $- 1$ by $100$ .

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

Step 6

Divide each term in $- 4 \cdot 5^{2 n + 1} = - 100$ by $- 4$ and simplify.

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Step 6.1

Divide each term in $- 4 \cdot 5^{2 n + 1} = - 100$ by $- 4$ .

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 4$ .

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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:

$n = 0.5$