Trigonometry Examples

${(x + 11)}^{2} = - 36$

Step 1

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

$x + 11 = \pm \sqrt{- 36}$

Step 2

Simplify $\pm \sqrt{- 36}$ .

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Step 2.1

Rewrite $- 36$ as $- 1 (36)$ .

$x + 11 = \pm \sqrt{- 1 (36)}$

Step 2.2

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$x + 11 = \pm \sqrt{- 1} \cdot \sqrt{36}$

Step 2.3

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

$x + 11 = \pm i \cdot \sqrt{36}$

Step 2.4

Rewrite $36$ as $6^{2}$ .

$x + 11 = \pm i \cdot \sqrt{6^{2}}$

Step 2.5

Pull terms out from under the radical, assuming positive real numbers.

$x + 11 = \pm i \cdot 6$

Step 2.6

Move $6$ to the left of $i$ .

$x + 11 = \pm 6 i$

Step 3

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

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Step 3.1

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

$x + 11 = 6 i$

Step 3.2

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

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Step 3.2.1

Subtract $11$ from both sides of the equation.

$x = 6 i - 11$

Step 3.2.2

Reorder $6 i$ and $- 11$ .

$x = - 11 + 6 i$

Step 3.3

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

$x + 11 = - 6 i$

Step 3.4

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

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Step 3.4.1

Subtract $11$ from both sides of the equation.

$x = - 6 i - 11$

Step 3.4.2

Reorder $- 6 i$ and $- 11$ .

$x = - 11 - 6 i$

Step 3.5

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

$x = - 11 + 6 i, - 11 - 6 i$