Pre-Algebra Examples

$17^{2} + x^{2} = 12^{2}$

Step 1

Raise $17$ to the power of $2$ .

$289 + x^{2} = 12^{2}$

Step 2

Raise $12$ to the power of $2$ .

$289 + x^{2} = 144$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $289$ from both sides of the equation.

$x^{2} = 144 - 289$

Step 3.2

Subtract $289$ from $144$ .

$x^{2} = - 145$

Step 4

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

$x = \pm \sqrt{- 145}$

Step 5

Simplify $\pm \sqrt{- 145}$ .

Tap for more steps...

Step 5.1

Rewrite $- 145$ as $- 1 (145)$ .

$x = \pm \sqrt{- 1 (145)}$

Step 5.2

Rewrite $\sqrt{- 1 (145)}$ as $\sqrt{- 1} \cdot \sqrt{145}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{145}$

Step 5.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{145}$

Step 6

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

Tap for more steps...

Step 6.1

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

$x = i \sqrt{145}$

Step 6.2

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

$x = - i \sqrt{145}$

Step 6.3

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

$x = i \sqrt{145}, - i \sqrt{145}$