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

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the exponent.

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$6 - 2 x = 4^{2}$

Simplify the right side.

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

$6 - 2 x = 16$

Step 4

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$- 2 x = 16 - 6$

Subtract $6$ from $16$ .

$- 2 x = 10$

Divide each term in $- 2 x = 10$ by $- 2$ and simplify.

Divide each term in $- 2 x = 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Divide $x$ by $1$ .

$x = \frac{10}{- 2}$

Simplify the right side.

Divide $10$ by $- 2$ .

$x = - 5$