Solve for c -70=-6-2c^2

$- 70 = - 6 - 2 c^{2}$

Step 1

Rewrite the equation as $- 6 - 2 c^{2} = - 70$ .

$- 6 - 2 c^{2} = - 70$

Step 2

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

Add $6$ to both sides of the equation.

$- 2 c^{2} = - 70 + 6$

Add $- 70$ and $6$ .

$- 2 c^{2} = - 64$

Step 3

Divide each term in $- 2 c^{2} = - 64$ by $- 2$ and simplify.

Divide each term in $- 2 c^{2} = - 64$ by $- 2$ .

$\frac{- 2 c^{2}}{- 2} = \frac{- 64}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 c^{2}}{- 2} = \frac{- 64}{- 2}$

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

$c^{2} = \frac{- 64}{- 2}$

Simplify the right side.

Divide $- 64$ by $- 2$ .

$c^{2} = 32$

Step 4

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

$c = \pm \sqrt{32}$

Step 5

Simplify $\pm \sqrt{32}$ .

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$c = \pm \sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$c = \pm \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$c = \pm 4 \sqrt{2}$

Step 6

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.

$c = 4 \sqrt{2}$

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

$c = - 4 \sqrt{2}$

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

$c = 4 \sqrt{2}, - 4 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$c = 4 \sqrt{2}, - 4 \sqrt{2}$

Decimal Form:

$c = 5.65685424 \dots, - 5.65685424 \dots$

Solve for c -70=-6-2c^2

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