Solve for x 36^(-2x+1)=216

$36^{- 2 x + 1} = 216$

Step 1

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

$6^{2 (- 2 x + 1)} = 6^{3}$

Step 2

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

$2 (- 2 x + 1) = 3$

Step 3

Solve for $x$ .

Divide each term in $2 (- 2 x + 1) = 3$ by $2$ and simplify.

Divide each term in $2 (- 2 x + 1) = 3$ by $2$ .

$\frac{2 (- 2 x + 1)}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (- 2 x + 1)}{2} = \frac{3}{2}$

Divide $- 2 x + 1$ by $1$ .

$- 2 x + 1 = \frac{3}{2}$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- 2 x = \frac{3}{2} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 x = \frac{3}{2} - 1 \cdot \frac{2}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

$- 2 x = \frac{3}{2} + \frac{- 1 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- 2 x = \frac{3 - 1 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$- 2 x = \frac{3 - 2}{2}$

Subtract $2$ from $3$ .

$- 2 x = \frac{1}{2}$

Divide each term in $- 2 x = \frac{1}{2}$ by $- 2$ and simplify.

Divide each term in $- 2 x = \frac{1}{2}$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{\frac{1}{2}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{\frac{1}{2}}{- 2}$

Divide $x$ by $1$ .

$x = \frac{\frac{1}{2}}{- 2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{2} \cdot \frac{1}{- 2}$

Move the negative in front of the fraction.

$x = \frac{1}{2} (- \frac{1}{2})$

Multiply $\frac{1}{2} (- \frac{1}{2})$ .

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$x = - \frac{1}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = - \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{4}$

Decimal Form:

$x = - 0.25$

Solve for x 36^(-2x+1)=216

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