Trigonometry Examples

$x^{2} - 10 + 25 = 0$

Step 1

Add $- 10$ and $25$ .

$x^{2} + 15 = 0$

Step 2

Subtract $15$ from both sides of the equation.

$x^{2} = - 15$

Step 3

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

$x = \pm \sqrt{- 15}$

Step 4

Simplify $\pm \sqrt{- 15}$ .

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Step 4.1

Rewrite $- 15$ as $- 1 (15)$ .

$x = \pm \sqrt{- 1 (15)}$

Step 4.2

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{15}$

Step 4.3

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

$x = \pm i \sqrt{15}$

Step 5

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

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Step 5.1

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

$x = i \sqrt{15}$

Step 5.2

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

$x = - i \sqrt{15}$

Step 5.3

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

$x = i \sqrt{15}, - i \sqrt{15}$