Solve for c 1/3c^2-10=17

$\frac{1}{3} c^{2} - 10 = 17$

Combine $\frac{1}{3}$ and $c^{2}$ .

$\frac{c^{2}}{3} - 10 = 17$

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

Add $10$ to both sides of the equation.

$\frac{c^{2}}{3} = 17 + 10$

Add $17$ and $10$ .

$\frac{c^{2}}{3} = 27$

Multiply both sides of the equation by $3$ .

$3 \frac{c^{2}}{3} = 3 \cdot 27$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{c^{2}}{3} = 3 \cdot 27$

Rewrite the expression.

$c^{2} = 3 \cdot 27$

Simplify the right side.

Multiply $3$ by $27$ .

$c^{2} = 81$

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

$c = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$c = \pm \sqrt{9^{2}}$

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

$c = \pm 9$

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.

$c = 9$

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

$c = - 9$

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

$c = 9, - 9$