Solve for v ((3*6)÷2)v+10=3^2v+9

$(3 \cdot 6 \div 2) v + 10 = 3^{2} v + 9$

Simplify $3 \cdot 6 \div 2 v + 10$ .

Multiply $3$ by $6$ .

$18 \div 2 v + 10 = 3^{2} v + 9$

Simplify each term.

Rewrite the division as a fraction.

$\frac{18}{2 v} + 10 = 3^{2} v + 9$

Cancel the common factor of $18$ and $2$ .

Factor $2$ out of $18$ .

$\frac{2 \cdot 9}{2 v} + 10 = 3^{2} v + 9$

Cancel the common factors.

Factor $2$ out of $2 v$ .

$\frac{2 \cdot 9}{2 (v)} + 10 = 3^{2} v + 9$

Cancel the common factor.

$\frac{2 \cdot 9}{2 v} + 10 = 3^{2} v + 9$

Rewrite the expression.

$\frac{9}{v} + 10 = 3^{2} v + 9$

Raise $3$ to the power of $2$ .

$\frac{9}{v} + 10 = 9 v + 9$

Subtract $9 v$ from both sides of the equation.

$\frac{9}{v} + 10 - 9 v = 9$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$v, 1, 1, 1$

The LCM of one and any expression is the expression.

$v$

Multiply each term in $\frac{9}{v} + 10 - 9 v = 9$ by $v$ to eliminate the fractions.

Multiply each term in $\frac{9}{v} + 10 - 9 v = 9$ by $v$ .

$\frac{9}{v} v + 10 v - 9 v \cdot v = 9 v$

Simplify the left side.

Simplify each term.

Cancel the common factor of $v$ .

Cancel the common factor.

$\frac{9}{v} v + 10 v - 9 v \cdot v = 9 v$

Rewrite the expression.

$9 + 10 v - 9 v \cdot v = 9 v$

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

$9 + 10 v - 9 (v \cdot v) = 9 v$

Multiply $v$ by $v$ .

$9 + 10 v - 9 v^{2} = 9 v$

Solve the equation.

Move all terms containing $v$ to the left side of the equation.

Subtract $9 v$ from both sides of the equation.

$9 + 10 v - 9 v^{2} - 9 v = 0$

Subtract $9 v$ from $10 v$ .

$9 - 9 v^{2} + v = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = - 9$ , $b = 1$ , and $c = 9$ into the quadratic formula and solve for $v$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (- 9 \cdot 9)}}{2 \cdot - 9}$

Simplify.

Simplify the numerator.

One to any power is one.

$v = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 9 \cdot 9}}{2 \cdot - 9}$

Multiply $- 4$ by $- 9$ .

$v = \frac{- 1 \pm \sqrt{1 + 36 \cdot 9}}{2 \cdot - 9}$

Multiply $36$ by $9$ .

$v = \frac{- 1 \pm \sqrt{1 + 324}}{2 \cdot - 9}$

Add $1$ and $324$ .

$v = \frac{- 1 \pm \sqrt{325}}{2 \cdot - 9}$

Rewrite $325$ as $5^{2} \cdot 13$ .

Factor $25$ out of $325$ .

$v = \frac{- 1 \pm \sqrt{25 (13)}}{2 \cdot - 9}$

Rewrite $25$ as $5^{2}$ .

$v = \frac{- 1 \pm \sqrt{5^{2} \cdot 13}}{2 \cdot - 9}$

Pull terms out from under the radical.

$v = \frac{- 1 \pm 5 \sqrt{13}}{2 \cdot - 9}$

Multiply $2$ by $- 9$ .

$v = \frac{- 1 \pm 5 \sqrt{13}}{- 18}$

Simplify $\frac{- 1 \pm 5 \sqrt{13}}{- 18}$ .

$v = \frac{1 \pm 5 \sqrt{13}}{18}$

The final answer is the combination of both solutions.

$v = \frac{1 + 5 \sqrt{13}}{18}, \frac{1 - 5 \sqrt{13}}{18}$

The result can be shown in multiple forms.

Exact Form:

$v = \frac{1 + 5 \sqrt{13}}{18}, \frac{1 - 5 \sqrt{13}}{18}$

Decimal Form:

$v = 1.05709757 \dots, - 0.94598646 \dots$

Solve for v ((3*6)÷2)v+10=3^2v+9

Related Questions

Support LCMGCF.com by disabling your adblocker.