Solve for x x^2+(2/3)^2=1

$x^{2} + {(\frac{2}{3})}^{2} = 1$

Step 1

Simplify each term.

Apply the product rule to $\frac{2}{3}$ .

$x^{2} + \frac{2^{2}}{3^{2}} = 1$

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

$x^{2} + \frac{4}{3^{2}} = 1$

Raise $3$ to the power of $2$ .

$x^{2} + \frac{4}{9} = 1$

Step 2

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

Subtract $\frac{4}{9}$ from both sides of the equation.

$x^{2} = 1 - \frac{4}{9}$

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

$x^{2} = \frac{9}{9} - \frac{4}{9}$

Combine the numerators over the common denominator.

$x^{2} = \frac{9 - 4}{9}$

Subtract $4$ from $9$ .

$x^{2} = \frac{5}{9}$

Step 3

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

$x = \pm \sqrt{\frac{5}{9}}$

Step 4

Simplify $\pm \sqrt{\frac{5}{9}}$ .

Rewrite $\sqrt{\frac{5}{9}}$ as $\frac{\sqrt{5}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{5}}{\sqrt{9}}$

Simplify the denominator.

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

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

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

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

Step 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.

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

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

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

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.74535599 \dots, - 0.74535599 \dots$