Pre-Algebra Examples

$x^{2} + 11^{2} = 9^{2}$

Step 1

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

$x^{2} + 121 = 9^{2}$

Step 2

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

$x^{2} + 121 = 81$

Step 3

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

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Step 3.1

Subtract $121$ from both sides of the equation.

$x^{2} = 81 - 121$

Step 3.2

Subtract $121$ from $81$ .

$x^{2} = - 40$

Step 4

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

$x = \pm \sqrt{- 40}$

Step 5

Simplify $\pm \sqrt{- 40}$ .

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Step 5.1

Rewrite $- 40$ as $- 1 (40)$ .

$x = \pm \sqrt{- 1 (40)}$

Step 5.2

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{40}$

Step 5.3

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

$x = \pm i \cdot \sqrt{40}$

Step 5.4

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 5.4.1

Factor $4$ out of $40$ .

$x = \pm i \cdot \sqrt{4 (10)}$

Step 5.4.2

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

$x = \pm i \cdot \sqrt{2^{2} \cdot 10}$

Step 5.5

Pull terms out from under the radical.

$x = \pm i \cdot (2 \sqrt{10})$

Step 5.6

Move $2$ to the left of $i$ .

$x = \pm 2 i \sqrt{10}$

Step 6

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

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Step 6.1

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

$x = 2 i \sqrt{10}$

Step 6.2

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

$x = - 2 i \sqrt{10}$

Step 6.3

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

$x = 2 i \sqrt{10}, - 2 i \sqrt{10}$