Solve for b -196=-4-3b^2

$- 196 = - 4 - 3 b^{2}$

Step 1

Rewrite the equation as $- 4 - 3 b^{2} = - 196$ .

$- 4 - 3 b^{2} = - 196$

Step 2

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

Add $4$ to both sides of the equation.

$- 3 b^{2} = - 196 + 4$

Add $- 196$ and $4$ .

$- 3 b^{2} = - 192$

Step 3

Divide each term in $- 3 b^{2} = - 192$ by $- 3$ and simplify.

Divide each term in $- 3 b^{2} = - 192$ by $- 3$ .

$\frac{- 3 b^{2}}{- 3} = \frac{- 192}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 b^{2}}{- 3} = \frac{- 192}{- 3}$

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

$b^{2} = \frac{- 192}{- 3}$

Simplify the right side.

Divide $- 192$ by $- 3$ .

$b^{2} = 64$

Step 4

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

$b = \pm \sqrt{64}$

Step 5

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$b = \pm \sqrt{8^{2}}$

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

$b = \pm 8$

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.

$b = 8$

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

$b = - 8$

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

$b = 8, - 8$