Pre-Algebra Examples

${(x + \frac{2}{3})}^{2} = \frac{4}{9}$

Step 1

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

$x + \frac{2}{3} = \pm \sqrt{\frac{4}{9}}$

Step 2

Simplify $\pm \sqrt{\frac{4}{9}}$ .

Tap for more steps...

Step 2.1

Rewrite $\sqrt{\frac{4}{9}}$ as $\frac{\sqrt{4}}{\sqrt{9}}$ .

$x + \frac{2}{3} = \pm \frac{\sqrt{4}}{\sqrt{9}}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Rewrite $4$ as $2^{2}$ .

$x + \frac{2}{3} = \pm \frac{\sqrt{2^{2}}}{\sqrt{9}}$

Step 2.2.2

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

$x + \frac{2}{3} = \pm \frac{2}{\sqrt{9}}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

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

$x + \frac{2}{3} = \pm \frac{2}{3}$

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$x = \frac{2}{3} - \frac{2}{3}$

Step 3.2.2

Combine the numerators over the common denominator.

$x = \frac{2 - 2}{3}$

Step 3.2.3

Subtract $2$ from $2$ .

$x = \frac{0}{3}$

Step 3.2.4

Divide $0$ by $3$ .

$x = 0$

Step 3.3

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

$x + \frac{2}{3} = - \frac{2}{3}$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$x = - \frac{2}{3} - \frac{2}{3}$

Step 3.4.2

Combine the numerators over the common denominator.

$x = \frac{- 2 - 2}{3}$

Step 3.4.3

Subtract $2$ from $- 2$ .

$x = \frac{- 4}{3}$

Step 3.4.4

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 3.5

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

$x = 0, - \frac{4}{3}$