Trigonometry Examples

${(x)}^{2} + {(24)}^{2} = {(7)}^{2}$

Step 1

Raise $24$ to the power of $2$ .

$x^{2} + 576 = 7^{2}$

Step 2

Raise $7$ to the power of $2$ .

$x^{2} + 576 = 49$

Step 3

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

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Step 3.1

Subtract $576$ from both sides of the equation.

$x^{2} = 49 - 576$

Step 3.2

Subtract $576$ from $49$ .

$x^{2} = - 527$

Step 4

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

$x = \pm \sqrt{- 527}$

Step 5

Simplify $\pm \sqrt{- 527}$ .

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Step 5.1

Rewrite $- 527$ as $- 1 (527)$ .

$x = \pm \sqrt{- 1 (527)}$

Step 5.2

Rewrite $\sqrt{- 1 (527)}$ as $\sqrt{- 1} \cdot \sqrt{527}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{527}$

Step 5.3

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

$x = \pm i \sqrt{527}$

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.

$x = i \sqrt{527}$

Step 6.2

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

$x = - i \sqrt{527}$

Step 6.3

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

$x = i \sqrt{527}, - i \sqrt{527}$