Solve for c -76=-3c^2-7

$- 76 = - 3 c^{2} - 7$

Step 1

Rewrite the equation as $- 3 c^{2} - 7 = - 76$ .

$- 3 c^{2} - 7 = - 76$

Step 2

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

Add $7$ to both sides of the equation.

$- 3 c^{2} = - 76 + 7$

Add $- 76$ and $7$ .

$- 3 c^{2} = - 69$

Step 3

Divide each term in $- 3 c^{2} = - 69$ by $- 3$ and simplify.

Divide each term in $- 3 c^{2} = - 69$ by $- 3$ .

$\frac{- 3 c^{2}}{- 3} = \frac{- 69}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 c^{2}}{- 3} = \frac{- 69}{- 3}$

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

$c^{2} = \frac{- 69}{- 3}$

Simplify the right side.

Divide $- 69$ by $- 3$ .

$c^{2} = 23$

Step 4

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

$c = \pm \sqrt{23}$

Step 5

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.

$c = \sqrt{23}$

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

$c = - \sqrt{23}$

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

$c = \sqrt{23}, - \sqrt{23}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt{23}, - \sqrt{23}$

Decimal Form:

$c = 4.79583152 \dots, - 4.79583152 \dots$