Solve for b 7+2b^2=79

$7 + 2 b^{2} = 79$

Step 1

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

Subtract $7$ from both sides of the equation.

$2 b^{2} = 79 - 7$

Subtract $7$ from $79$ .

$2 b^{2} = 72$

Step 2

Divide each term in $2 b^{2} = 72$ by $2$ and simplify.

Divide each term in $2 b^{2} = 72$ by $2$ .

$\frac{2 b^{2}}{2} = \frac{72}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b^{2}}{2} = \frac{72}{2}$

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

$b^{2} = \frac{72}{2}$

Simplify the right side.

Divide $72$ by $2$ .

$b^{2} = 36$

Step 3

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

$b = \pm \sqrt{36}$

Step 4

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$b = \pm \sqrt{6^{2}}$

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

$b = \pm 6$

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.

$b = 6$

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

$b = - 6$

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

$b = 6, - 6$