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

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

Move $\sqrt{x - 2}$ to the left side of the equation by subtracting it from both sides.

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

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

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

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

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

Simplify each side of the equation.

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Multiply the exponents in ${({(11 - 3 x)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

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

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

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

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

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

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

$11 - 3 x = {(x - 2)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$11 - 3 x = {(x - 2)}^{\frac{2}{2}}$

Divide $1$ by $1$ .

$11 - 3 x = {(x - 2)}^{1}$

Simplify.

$11 - 3 x = x - 2$

Solve for $x$ .

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

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Subtract $x$ from both sides of the equation.

$11 - 3 x - x = - 2$

Subtract $x$ from $- 3 x$ .

$11 - 4 x = - 2$

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

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Subtract $11$ from both sides of the equation.

$- 4 x = - 2 - 11$

Subtract $11$ from $- 2$ .

$- 4 x = - 13$

Divide each term by $- 4$ and simplify.

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Divide each term in $- 4 x = - 13$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 13}{- 4}$

Cancel the common factor of $- 4$ .

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Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 13}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 13}{- 4}$

Dividing two negative values results in a positive value.

$x = \frac{13}{4}$

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

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