Solve for b 5^2+b^2=9^2

$5^{2} + b^{2} = 9^{2}$

Step 1

Raise $5$ to the power of $2$ .

$25 + b^{2} = 9^{2}$

Step 2

Raise $9$ to the power of $2$ .

$25 + b^{2} = 81$

Step 3

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

Subtract $25$ from both sides of the equation.

$b^{2} = 81 - 25$

Subtract $25$ from $81$ .

$b^{2} = 56$

Step 4

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

$b = \pm \sqrt{56}$

Step 5

Simplify $\pm \sqrt{56}$ .

Rewrite $56$ as $2^{2} \cdot 14$ .

Factor $4$ out of $56$ .

$b = \pm \sqrt{4 (14)}$

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

$b = \pm \sqrt{2^{2} \cdot 14}$

Pull terms out from under the radical.

$b = \pm 2 \sqrt{14}$

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.

$b = 2 \sqrt{14}$

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

$b = - 2 \sqrt{14}$

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

$b = 2 \sqrt{14}, - 2 \sqrt{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = 2 \sqrt{14}, - 2 \sqrt{14}$

Decimal Form:

$b = 7.48331477 \dots, - 7.48331477 \dots$