Solve for c 92=2+10c^2

$92 = 2 + 10 c^{2}$

Rewrite the equation as $2 + 10 c^{2} = 92$ .

$2 + 10 c^{2} = 92$

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

Subtract $2$ from both sides of the equation.

$10 c^{2} = 92 - 2$

Subtract $2$ from $92$ .

$10 c^{2} = 90$

Divide each term in $10 c^{2} = 90$ by $10$ and simplify.

Divide each term in $10 c^{2} = 90$ by $10$ .

$\frac{10 c^{2}}{10} = \frac{90}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 c^{2}}{10} = \frac{90}{10}$

Divide $c^{2}$ by $1$ .

$c^{2} = \frac{90}{10}$

Simplify the right side.

Divide $90$ by $10$ .

$c^{2} = 9$

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

$c = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$c = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$c = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$c = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 3, - 3$