Algebra Examples

$\sqrt{2 x} - \frac{2}{3} = 0$

Step 1

Add $\frac{2}{3}$ to both sides of the equation.

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

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

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

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(2 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(2 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

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

Step 3.2.1.2

Simplify.

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(\frac{2}{3})}^{2}$ .

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Step 3.3.1.1

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

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

Step 3.3.1.2

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

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

Step 3.3.1.3

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

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

Step 4

Divide each term in $2 x = \frac{4}{9}$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = \frac{4}{9}$ by $2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{4}{9} \cdot \frac{1}{2}$

Step 4.3.2

Cancel the common factor of $2$ .

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Step 4.3.2.1

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{9} \cdot \frac{1}{2}$

Step 4.3.2.2

Cancel the common factor.

$x = \frac{2 \cdot 2}{9} \cdot \frac{1}{2}$

Step 4.3.2.3

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{2}$