Solve for x x^2+(-8/17)^2=1

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

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{8}{17}$ .

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

Apply the product rule to $\frac{8}{17}$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply $\frac{8^{2}}{17^{2}}$ by $1$ .

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

Raise $8$ to the power of $2$ .

$x^{2} + \frac{64}{17^{2}} = 1$

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

$x^{2} + \frac{64}{289} = 1$

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

Subtract $\frac{64}{289}$ from both sides of the equation.

$x^{2} = 1 - \frac{64}{289}$

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

$x^{2} = \frac{289}{289} - \frac{64}{289}$

Combine the numerators over the common denominator.

$x^{2} = \frac{289 - 64}{289}$

Subtract $64$ from $289$ .

$x^{2} = \frac{225}{289}$

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

$x = \pm \sqrt{\frac{225}{289}}$

Simplify $\pm \sqrt{\frac{225}{289}}$ .

Rewrite $\sqrt{\frac{225}{289}}$ as $\frac{\sqrt{225}}{\sqrt{289}}$ .

$x = \pm \frac{\sqrt{225}}{\sqrt{289}}$

Simplify the numerator.

Rewrite $225$ as $15^{2}$ .

$x = \pm \frac{\sqrt{15^{2}}}{\sqrt{289}}$

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

$x = \pm \frac{15}{\sqrt{289}}$

Simplify the denominator.

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

$x = \pm \frac{15}{\sqrt{17^{2}}}$

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

$x = \pm \frac{15}{17}$

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

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

$x = \frac{15}{17}$

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

$x = - \frac{15}{17}$

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

$x = \frac{15}{17}, - \frac{15}{17}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{17}, - \frac{15}{17}$

Decimal Form:

$x = 0.88235294 \dots, - 0.88235294 \dots$

Solve for x x^2+(-8/17)^2=1

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