Trigonometry Examples

$5^{2} + 4^{2} = x^{2}$

Step 1

Rewrite the equation as $x^{2} = 5^{2} + 4^{2}$ .

$x^{2} = 5^{2} + 4^{2}$

Step 2

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

$x = \pm \sqrt{5^{2} + 4^{2}}$

Step 3

Simplify $\pm \sqrt{5^{2} + 4^{2}}$ .

Tap for more steps...

Step 3.1

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

$x = \pm \sqrt{25 + 4^{2}}$

Step 3.2

Raise $4$ to the power of $2$ .

$x = \pm \sqrt{25 + 16}$

Step 3.3

Add $25$ and $16$ .

$x = \pm \sqrt{41}$

Step 4

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

Tap for more steps...

Step 4.1

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

$x = \sqrt{41}$

Step 4.2

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

$x = - \sqrt{41}$

Step 4.3

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

$x = \sqrt{41}, - \sqrt{41}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{41}, - \sqrt{41}$

Decimal Form:

$x = 6.40312423 \dots, - 6.40312423 \dots$