Algebra Examples

$2 \sqrt{x + 8} = 3 \sqrt{x - 2}$

Step 1

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

${(2 \sqrt{x + 8})}^{2} = {(3 \sqrt{x - 2})}^{2}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 8}$ as ${(x + 8)}^{\frac{1}{2}}$ .

${(2 {(x + 8)}^{\frac{1}{2}})}^{2} = {(3 \sqrt{x - 2})}^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${(2 {(x + 8)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Apply the product rule to $2 {(x + 8)}^{\frac{1}{2}}$ .

$2^{2} {({(x + 8)}^{\frac{1}{2}})}^{2} = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.2

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

$4 {({(x + 8)}^{\frac{1}{2}})}^{2} = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.3

Multiply the exponents in ${({(x + 8)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.3.1

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

$4 {(x + 8)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.3.2.1

Cancel the common factor.

$4 {(x + 8)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.3.2.2

Rewrite the expression.

$4 {(x + 8)}^{1} = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.4

Simplify.

$4 (x + 8) = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.5

Apply the distributive property.

$4 x + 4 \cdot 8 = {(3 \sqrt{x - 2})}^{2}$

Step 2.2.1.6

Multiply $4$ by $8$ .

$4 x + 32 = {(3 \sqrt{x - 2})}^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify ${(3 \sqrt{x - 2})}^{2}$ .

Tap for more steps...

Step 2.3.1.1

Simplify the expression.

Tap for more steps...

Step 2.3.1.1.1

Apply the product rule to $3 \sqrt{x - 2}$ .

$4 x + 32 = 3^{2} {\sqrt{x - 2}}^{2}$

Step 2.3.1.1.2

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

$4 x + 32 = 9 {\sqrt{x - 2}}^{2}$

Step 2.3.1.2

Rewrite ${\sqrt{x - 2}}^{2}$ as $x - 2$ .

Tap for more steps...

Step 2.3.1.2.1

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

$4 x + 32 = 9 {({(x - 2)}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2.2

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

$4 x + 32 = 9 {(x - 2)}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.2.3

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

$4 x + 32 = 9 {(x - 2)}^{\frac{2}{2}}$

Step 2.3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.2.4.1

Cancel the common factor.

$4 x + 32 = 9 {(x - 2)}^{\frac{2}{2}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$4 x + 32 = 9 {(x - 2)}^{1}$

Step 2.3.1.2.5

Simplify.

$4 x + 32 = 9 (x - 2)$

Step 2.3.1.3

Apply the distributive property.

$4 x + 32 = 9 x + 9 \cdot - 2$

Step 2.3.1.4

Multiply $9$ by $- 2$ .

$4 x + 32 = 9 x - 18$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $9 x$ from both sides of the equation.

$4 x + 32 - 9 x = - 18$

Step 3.1.2

Subtract $9 x$ from $4 x$ .

$- 5 x + 32 = - 18$

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 $32$ from both sides of the equation.

$- 5 x = - 18 - 32$

Step 3.2.2

Subtract $32$ from $- 18$ .

$- 5 x = - 50$

Step 3.3

Divide each term in $- 5 x = - 50$ by $- 5$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 5 x = - 50$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 50}{- 5}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 50}{- 5}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 50}{- 5}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $- 50$ by $- 5$ .

$x = 10$