Solve for b 10+5b^2=200

$10 + 5 b^{2} = 200$

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

Subtract $10$ from both sides of the equation.

$5 b^{2} = 200 - 10$

Subtract $10$ from $200$ .

$5 b^{2} = 190$

Divide each term in $5 b^{2} = 190$ by $5$ and simplify.

Divide each term in $5 b^{2} = 190$ by $5$ .

$\frac{5 b^{2}}{5} = \frac{190}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 b^{2}}{5} = \frac{190}{5}$

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

$b^{2} = \frac{190}{5}$

Simplify the right side.

Divide $190$ by $5$ .

$b^{2} = 38$

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

$b = \pm \sqrt{38}$

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.

$b = \sqrt{38}$

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

$b = - \sqrt{38}$

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

$b = \sqrt{38}, - \sqrt{38}$

The result can be shown in multiple forms.

Exact Form:

$b = \sqrt{38}, - \sqrt{38}$

Decimal Form:

$b = 6.16441400 \dots, - 6.16441400 \dots$