Solve the Rational Equation for x 2 square root of 3x+9-4=20

$2 \sqrt{3 x + 9} - 4 = 20$

Move all terms not containing $2 \sqrt{3 x + 9}$ to the right side of the equation.

Add $4$ to both sides of the equation.

$2 \sqrt{3 x + 9} = 20 + 4$

Add $20$ and $4$ .

$2 \sqrt{3 x + 9} = 24$

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

${(2 \sqrt{3 x + 9})}^{2} = 24^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x + 9}$ as ${(3 x + 9)}^{\frac{1}{2}}$ .

${(2 {(3 x + 9)}^{\frac{1}{2}})}^{2} = 24^{2}$

Simplify the left side.

Simplify ${(2 {(3 x + 9)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $2 {(3 x + 9)}^{\frac{1}{2}}$ .

$2^{2} {({(3 x + 9)}^{\frac{1}{2}})}^{2} = 24^{2}$

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

$4 {({(3 x + 9)}^{\frac{1}{2}})}^{2} = 24^{2}$

Multiply the exponents in ${({(3 x + 9)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(3 x + 9)}^{\frac{1}{2} \cdot 2} = 24^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(3 x + 9)}^{\frac{1}{2} \cdot 2} = 24^{2}$

Rewrite the expression.

$4 {(3 x + 9)}^{1} = 24^{2}$

Simplify.

$4 (3 x + 9) = 24^{2}$

Apply the distributive property.

$4 (3 x) + 4 \cdot 9 = 24^{2}$

Multiply.

Multiply $3$ by $4$ .

$12 x + 4 \cdot 9 = 24^{2}$

Multiply $4$ by $9$ .

$12 x + 36 = 24^{2}$

Simplify the right side.

Raise $24$ to the power of $2$ .

$12 x + 36 = 576$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $36$ from both sides of the equation.

$12 x = 576 - 36$

Subtract $36$ from $576$ .

$12 x = 540$

Divide each term in $12 x = 540$ by $12$ and simplify.

Divide each term in $12 x = 540$ by $12$ .

$\frac{12 x}{12} = \frac{540}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{540}{12}$

Divide $x$ by $1$ .

$x = \frac{540}{12}$

Simplify the right side.

Divide $540$ by $12$ .

$x = 45$

Solve the Rational Equation for x 2 square root of 3x+9-4=20

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