Solve for x square root of 3x-3 square root of x+4=0

$\sqrt{3 x} - 3 \sqrt{x + 4} = 0$

Add $3 \sqrt{x + 4}$ to both sides of the equation.

$\sqrt{3 x} = 3 \sqrt{x + 4}$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(3 \sqrt{x + 4})}^{2}$ .

Simplify the expression.

Apply the product rule to $3 \sqrt{x + 4}$ .

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

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

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

Rewrite ${\sqrt{x + 4}}^{2}$ as $x + 4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 4}$ as ${(x + 4)}^{\frac{1}{2}}$ .

$3 x = 9 {({(x + 4)}^{\frac{1}{2}})}^{2}$

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

$3 x = 9 {(x + 4)}^{\frac{1}{2} \cdot 2}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x = 9 {(x + 4)}^{1}$

Simplify.

$3 x = 9 (x + 4)$

Apply the distributive property.

$3 x = 9 x + 9 \cdot 4$

Multiply $9$ by $4$ .

$3 x = 9 x + 36$

Solve for $x$ .

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

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

$3 x - 9 x = 36$

Subtract $9 x$ from $3 x$ .

$- 6 x = 36$

Divide each term in $- 6 x = 36$ by $- 6$ and simplify.

Divide each term in $- 6 x = 36$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{36}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{36}{- 6}$

Divide $x$ by $1$ .

$x = \frac{36}{- 6}$

Simplify the right side.

Divide $36$ by $- 6$ .

$x = - 6$

Exclude the solutions that do not make $\sqrt{3 x} - 3 \sqrt{x + 4} = 0$ true.

$No solution$

Solve for x square root of 3x-3 square root of x+4=0

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