Precalculus Examples

$3^{2} + b^{2} = 8^{2}$

Step 1

Raise $3$ to the power of $2$ .

$9 + b^{2} = 8^{2}$

Step 2

Raise $8$ to the power of $2$ .

$9 + b^{2} = 64$

Step 3

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

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Step 3.1

Subtract $9$ from both sides of the equation.

$b^{2} = 64 - 9$

Step 3.2

Subtract $9$ from $64$ .

$b^{2} = 55$

Step 4

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

$b = \pm \sqrt{55}$

Step 5

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

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$b = \sqrt{55}$

Step 5.2

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

$b = - \sqrt{55}$

Step 5.3

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

$b = \sqrt{55}, - \sqrt{55}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \sqrt{55}, - \sqrt{55}$

Decimal Form:

$b = 7.41619848 \dots, - 7.41619848 \dots$