Solve by Factoring square root of 11x=3 square root of x+2

$\sqrt{11 x} = 3 \sqrt{x + 2}$

Step 1

Subtract $3 \sqrt{x + 2}$ from both sides of the equation.

$\sqrt{11 x} - 3 \sqrt{x + 2} = 0$

Step 2

Add $3 \sqrt{x + 2}$ to both sides of the equation.

$\sqrt{11 x} = 3 \sqrt{x + 2}$

Step 3

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

${\sqrt{11 x}}^{2} = {(3 \sqrt{x + 2})}^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11 x}$ as ${(11 x)}^{\frac{1}{2}}$ .

${({(11 x)}^{\frac{1}{2}})}^{2} = {(3 \sqrt{x + 2})}^{2}$

Simplify the left side.

Simplify ${({(11 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(11 x)}^{\frac{1}{2}})}^{2}$ .

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

${(11 x)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{x + 2})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(11 x)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{x + 2})}^{2}$

Rewrite the expression.

${(11 x)}^{1} = {(3 \sqrt{x + 2})}^{2}$

Simplify.

$11 x = {(3 \sqrt{x + 2})}^{2}$

Simplify the right side.

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

Simplify the expression.

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

$11 x = 3^{2} {\sqrt{x + 2}}^{2}$

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

$11 x = 9 {\sqrt{x + 2}}^{2}$

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

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

$11 x = 9 {({(x + 2)}^{\frac{1}{2}})}^{2}$

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

$11 x = 9 {(x + 2)}^{\frac{1}{2} \cdot 2}$

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

$11 x = 9 {(x + 2)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$11 x = 9 {(x + 2)}^{\frac{2}{2}}$

Rewrite the expression.

$11 x = 9 {(x + 2)}^{1}$

Simplify.

$11 x = 9 (x + 2)$

Apply the distributive property.

$11 x = 9 x + 9 \cdot 2$

Multiply $9$ by $2$ .

$11 x = 9 x + 18$

Step 5

Solve for $x$ .

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

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

$11 x - 9 x = 18$

Subtract $9 x$ from $11 x$ .

$2 x = 18$

Divide each term in $2 x = 18$ by $2$ and simplify.

Divide each term in $2 x = 18$ by $2$ .

$\frac{2 x}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{18}{2}$

Divide $x$ by $1$ .

$x = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x = 9$

Solve by Factoring square root of 11x=3 square root of x+2

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