Solve for x square root of 4x-20+3 square root of (x-5)/9-1/3 square root of 9x-45=4

$\sqrt{4 x - 20} + 3 \sqrt{\frac{x - 5}{9}} - \frac{1}{3} \sqrt{9 x - 45} = 4$

Simplify $\sqrt{4 x - 20} + 3 \sqrt{\frac{x - 5}{9}} - \frac{1}{3} \cdot \sqrt{9 x - 45}$ .

Simplify each term.

Rewrite $\frac{x - 5}{9}$ as ${(\frac{1}{3})}^{2} (x - 5)$ .

Factor the perfect power $1^{2}$ out of $x - 5$ .

$\sqrt{4 x - 20} + 3 \sqrt{\frac{1^{2} (x - 5)}{9}} - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Factor the perfect power $3^{2}$ out of $9$ .

$\sqrt{4 x - 20} + 3 \sqrt{\frac{1^{2} (x - 5)}{3^{2} \cdot 1}} - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Rearrange the fraction $\frac{1^{2} (x - 5)}{3^{2} \cdot 1}$ .

$\sqrt{4 x - 20} + 3 \sqrt{{(\frac{1}{3})}^{2} (x - 5)} - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Pull terms out from under the radical.

$\sqrt{4 x - 20} + 3 (\frac{1}{3} \sqrt{x - 5}) - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Combine $\frac{1}{3}$ and $\sqrt{x - 5}$ .

$\sqrt{4 x - 20} + 3 \frac{\sqrt{x - 5}}{3} - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Cancel the common factor of $3$ .

Cancel the common factor.

$\sqrt{4 x - 20} + 3 \frac{\sqrt{x - 5}}{3} - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Rewrite the expression.

$\sqrt{4 x - 20} + \sqrt{x - 5} - \frac{1}{3} \cdot \sqrt{9 x - 45} = 4$

Factor $9$ out of $9 x - 45$ .

Factor $9$ out of $9 x$ .

$\sqrt{4 x - 20} + \sqrt{x - 5} - \frac{1}{3} \cdot \sqrt{9 (x) - 45} = 4$

Factor $9$ out of $- 45$ .

$\sqrt{4 x - 20} + \sqrt{x - 5} - \frac{1}{3} \cdot \sqrt{9 x + 9 \cdot - 5} = 4$

Factor $9$ out of $9 x + 9 \cdot - 5$ .

$\sqrt{4 x - 20} + \sqrt{x - 5} - \frac{1}{3} \cdot \sqrt{9 (x - 5)} = 4$

Rewrite $9$ as $3^{2}$ .

$\sqrt{4 x - 20} + \sqrt{x - 5} - \frac{1}{3} \cdot \sqrt{3^{2} (x - 5)} = 4$

Pull terms out from under the radical.

$\sqrt{4 x - 20} + \sqrt{x - 5} - \frac{1}{3} \cdot (3 \sqrt{x - 5}) = 4$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\sqrt{4 x - 20} + \sqrt{x - 5} + \frac{- 1}{3} \cdot (3 \sqrt{x - 5}) = 4$

Factor $3$ out of $3 \sqrt{x - 5}$ .

$\sqrt{4 x - 20} + \sqrt{x - 5} + \frac{- 1}{3} \cdot (3 (\sqrt{x - 5})) = 4$

Cancel the common factor.

$\sqrt{4 x - 20} + \sqrt{x - 5} + \frac{- 1}{3} \cdot (3 \sqrt{x - 5}) = 4$

Rewrite the expression.

$\sqrt{4 x - 20} + \sqrt{x - 5} - 1 \cdot \sqrt{x - 5} = 4$

Rewrite $- 1 \sqrt{x - 5}$ as $- \sqrt{x - 5}$ .

$\sqrt{4 x - 20} + \sqrt{x - 5} - \sqrt{x - 5} = 4$

Combine the opposite terms in $\sqrt{4 x - 20} + \sqrt{x - 5} - \sqrt{x - 5}$ .

Subtract $\sqrt{x - 5}$ from $\sqrt{x - 5}$ .

$\sqrt{4 x - 20} + 0 = 4$

Add $\sqrt{4 x - 20}$ and $0$ .

$\sqrt{4 x - 20} = 4$

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

${\sqrt{4 x - 20}}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x - 20}$ as ${(4 x - 20)}^{\frac{1}{2}}$ .

${({(4 x - 20)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(4 x - 20)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x - 20)}^{\frac{1}{2}})}^{2}$ .

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

${(4 x - 20)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x - 20)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(4 x - 20)}^{1} = 4^{2}$

Simplify.

$4 x - 20 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$4 x - 20 = 16$

Solve for $x$ .

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

Add $20$ to both sides of the equation.

$4 x = 16 + 20$

Add $16$ and $20$ .

$4 x = 36$

Divide each term in $4 x = 36$ by $4$ and simplify.

Divide each term in $4 x = 36$ by $4$ .

$\frac{4 x}{4} = \frac{36}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{36}{4}$

Divide $x$ by $1$ .

$x = \frac{36}{4}$

Simplify the right side.

Divide $36$ by $4$ .

$x = 9$

Solve for x square root of 4x-20+3 square root of (x-5)/9-1/3 square root of 9x-45=4

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