Solve for c 9c^2+14=43

$9 c^{2} + 14 = 43$

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

Subtract $14$ from both sides of the equation.

$9 c^{2} = 43 - 14$

Subtract $14$ from $43$ .

$9 c^{2} = 29$

Divide each term in $9 c^{2} = 29$ by $9$ and simplify.

Divide each term in $9 c^{2} = 29$ by $9$ .

$\frac{9 c^{2}}{9} = \frac{29}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 c^{2}}{9} = \frac{29}{9}$

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

$c^{2} = \frac{29}{9}$

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

$c = \pm \sqrt{\frac{29}{9}}$

Simplify $\pm \sqrt{\frac{29}{9}}$ .

Rewrite $\sqrt{\frac{29}{9}}$ as $\frac{\sqrt{29}}{\sqrt{9}}$ .

$c = \pm \frac{\sqrt{29}}{\sqrt{9}}$

Simplify the denominator.

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

$c = \pm \frac{\sqrt{29}}{\sqrt{3^{2}}}$

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

$c = \pm \frac{\sqrt{29}}{3}$

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.

$c = \frac{\sqrt{29}}{3}$

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

$c = - \frac{\sqrt{29}}{3}$

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

$c = \frac{\sqrt{29}}{3}, - \frac{\sqrt{29}}{3}$

The result can be shown in multiple forms.

Exact Form:

$c = \frac{\sqrt{29}}{3}, - \frac{\sqrt{29}}{3}$

Decimal Form:

$c = 1.79505493 \dots, - 1.79505493 \dots$