Solve for x x^2+(-4/5)^2=1

$x^{2} + {(- \frac{4}{5})}^{2} = 1$

Simplify each term.

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

Apply the product rule to $- \frac{4}{5}$ .

$x^{2} + {(- 1)}^{2} {(\frac{4}{5})}^{2} = 1$

Apply the product rule to $\frac{4}{5}$ .

$x^{2} + {(- 1)}^{2} \frac{4^{2}}{5^{2}} = 1$

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

$x^{2} + 1 \frac{4^{2}}{5^{2}} = 1$

Multiply $\frac{4^{2}}{5^{2}}$ by $1$ .

$x^{2} + \frac{4^{2}}{5^{2}} = 1$

Raise $4$ to the power of $2$ .

$x^{2} + \frac{16}{5^{2}} = 1$

Raise $5$ to the power of $2$ .

$x^{2} + \frac{16}{25} = 1$

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

Subtract $\frac{16}{25}$ from both sides of the equation.

$x^{2} = 1 - \frac{16}{25}$

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

$x^{2} = \frac{25}{25} - \frac{16}{25}$

Combine the numerators over the common denominator.

$x^{2} = \frac{25 - 16}{25}$

Subtract $16$ from $25$ .

$x^{2} = \frac{9}{25}$

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

$x = \pm \sqrt{\frac{9}{25}}$

Simplify $\pm \sqrt{\frac{9}{25}}$ .

Rewrite $\sqrt{\frac{9}{25}}$ as $\frac{\sqrt{9}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{9}}{\sqrt{25}}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$x = \pm \frac{\sqrt{3^{2}}}{\sqrt{25}}$

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

$x = \pm \frac{3}{\sqrt{25}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{3}{\sqrt{5^{2}}}$

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

$x = \pm \frac{3}{5}$

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.

$x = \frac{3}{5}$

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

$x = - \frac{3}{5}$

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

$x = \frac{3}{5}, - \frac{3}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{5}, - \frac{3}{5}$

Decimal Form:

$x = 0.6, - 0.6$

Solve for x x^2+(-4/5)^2=1

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