Solve for x 3=11-(4-6x)^(1/2)

$3 = 11 - {(4 - 6 x)}^{\frac{1}{2}}$

Rewrite the equation as $11 - {(4 - 6 x)}^{\frac{1}{2}} = 3$ .

$11 - {(4 - 6 x)}^{\frac{1}{2}} = 3$

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

Subtract $11$ from both sides of the equation.

$- {(4 - 6 x)}^{\frac{1}{2}} = 3 - 11$

Subtract $11$ from $3$ .

$- {(4 - 6 x)}^{\frac{1}{2}} = - 8$

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(- {(4 - 6 x)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Simplify the exponent.

Simplify the left side.

Simplify ${(- {(4 - 6 x)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- {(4 - 6 x)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(4 - 6 x)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Raise $- 1$ to the power of $2$ .

$1 {({(4 - 6 x)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Multiply ${({(4 - 6 x)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(4 - 6 x)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Multiply the exponents in ${({(4 - 6 x)}^{\frac{1}{2}})}^{2}$ .

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

${(4 - 6 x)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 - 6 x)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Rewrite the expression.

${(4 - 6 x)}^{1} = {(- 8)}^{2}$

Simplify.

$4 - 6 x = {(- 8)}^{2}$

Simplify the right side.

Raise $- 8$ to the power of $2$ .

$4 - 6 x = 64$

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$- 6 x = 64 - 4$

Subtract $4$ from $64$ .

$- 6 x = 60$

Divide each term in $- 6 x = 60$ by $- 6$ and simplify.

Divide each term in $- 6 x = 60$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{60}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{60}{- 6}$

Divide $x$ by $1$ .

$x = \frac{60}{- 6}$

Simplify the right side.

Divide $60$ by $- 6$ .

$x = - 10$

Solve for x 3=11-(4-6x)^(1/2)

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