Trigonometry Examples

$x^{2} + \frac{8}{17^{2}} = 1$

Step 1

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

$x^{2} + \frac{8}{289} = 1$

Step 2

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

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Step 2.1

Subtract $\frac{8}{289}$ from both sides of the equation.

$x^{2} = 1 - \frac{8}{289}$

Step 2.2

Write $1$ as a fraction with a common denominator.

$x^{2} = \frac{289}{289} - \frac{8}{289}$

Step 2.3

Combine the numerators over the common denominator.

$x^{2} = \frac{289 - 8}{289}$

Step 2.4

Subtract $8$ from $289$ .

$x^{2} = \frac{281}{289}$

Step 3

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

$x = \pm \sqrt{\frac{281}{289}}$

Step 4

Simplify $\pm \sqrt{\frac{281}{289}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{281}{289}}$ as $\frac{\sqrt{281}}{\sqrt{289}}$ .

$x = \pm \frac{\sqrt{281}}{\sqrt{289}}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Rewrite $289$ as $17^{2}$ .

$x = \pm \frac{\sqrt{281}}{\sqrt{17^{2}}}$

Step 4.2.2

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

$x = \pm \frac{\sqrt{281}}{17}$

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.

$x = \frac{\sqrt{281}}{17}$

Step 5.2

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

$x = - \frac{\sqrt{281}}{17}$

Step 5.3

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

$x = \frac{\sqrt{281}}{17}, - \frac{\sqrt{281}}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{281}}{17}, - \frac{\sqrt{281}}{17}$

Decimal Form:

$x = 0.98606203 \dots, - 0.98606203 \dots$