Solve for x 11^2+10^2=x^2

$11^{2} + 10^{2} = x^{2}$

Step 1

Rewrite the equation as $x^{2} = 11^{2} + 10^{2}$ .

$x^{2} = 11^{2} + 10^{2}$

Step 2

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

$x = \pm \sqrt{11^{2} + 10^{2}}$

Step 3

Simplify $\pm \sqrt{11^{2} + 10^{2}}$ .

Raise $11$ to the power of $2$ .

$x = \pm \sqrt{121 + 10^{2}}$

Raise $10$ to the power of $2$ .

$x = \pm \sqrt{121 + 100}$

Add $121$ and $100$ .

$x = \pm \sqrt{221}$

Step 4

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.

$x = \sqrt{221}$

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

$x = - \sqrt{221}$

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

$x = \sqrt{221}, - \sqrt{221}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{221}, - \sqrt{221}$

Decimal Form:

$x = 14.86606874 \dots, - 14.86606874 \dots$