Algebra Examples

$\sqrt{3 x} = \sqrt{x + 6}$

Step 1

Subtract $\sqrt{x + 6}$ from both sides of the equation.

$\sqrt{3 x} - \sqrt{x + 6} = 0$

Step 2

Add $\sqrt{x + 6}$ to both sides of the equation.

$\sqrt{3 x} = \sqrt{x + 6}$

Step 3

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

${\sqrt{3 x}}^{2} = {\sqrt{x + 6}}^{2}$

Step 4

Simplify each side of the equation.

Tap for more steps...

Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

${({(3 x)}^{\frac{1}{2}})}^{2} = {\sqrt{x + 6}}^{2}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

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

Tap for more steps...

Step 4.2.1.1

Multiply the exponents in ${({(3 x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 4.2.1.1.1

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

${(3 x)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 6}}^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1.2.1

Cancel the common factor.

${(3 x)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 6}}^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(3 x)}^{1} = {\sqrt{x + 6}}^{2}$

Step 4.2.1.2

Simplify.

$3 x = {\sqrt{x + 6}}^{2}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Rewrite ${\sqrt{x + 6}}^{2}$ as $x + 6$ .

Tap for more steps...

Step 4.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 6}$ as ${(x + 6)}^{\frac{1}{2}}$ .

$3 x = {({(x + 6)}^{\frac{1}{2}})}^{2}$

Step 4.3.1.2

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

$3 x = {(x + 6)}^{\frac{1}{2} \cdot 2}$

Step 4.3.1.3

Combine $\frac{1}{2}$ and $2$ .

$3 x = {(x + 6)}^{\frac{2}{2}}$

Step 4.3.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.3.1.4.1

Cancel the common factor.

$3 x = {(x + 6)}^{\frac{2}{2}}$

Step 4.3.1.4.2

Rewrite the expression.

$3 x = {(x + 6)}^{1}$

Step 4.3.1.5

Simplify.

$3 x = x + 6$

Step 5

Solve for $x$ .

Tap for more steps...

Step 5.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 5.1.1

Subtract $x$ from both sides of the equation.

$3 x - x = 6$

Step 5.1.2

Subtract $x$ from $3 x$ .

$2 x = 6$

Step 5.2

Divide each term in $2 x = 6$ by $2$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Divide $6$ by $2$ .

$x = 3$