Solve for n -4=-8+ square root of 32-2n

$- 4 = - 8 + \sqrt{32 - 2 n}$

Rewrite the equation as $- 8 + \sqrt{32 - 2 n} = - 4$ .

$- 8 + \sqrt{32 - 2 n} = - 4$

Move all terms not containing $\sqrt{32 - 2 n}$ to the right side of the equation.

Add $8$ to both sides of the equation.

$\sqrt{32 - 2 n} = - 4 + 8$

Add $- 4$ and $8$ .

$\sqrt{32 - 2 n} = 4$

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

${\sqrt{32 - 2 n}}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{32 - 2 n}$ as ${(32 - 2 n)}^{\frac{1}{2}}$ .

${({(32 - 2 n)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(32 - 2 n)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(32 - 2 n)}^{\frac{1}{2}})}^{2}$ .

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

${(32 - 2 n)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(32 - 2 n)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(32 - 2 n)}^{1} = 4^{2}$

Simplify.

$32 - 2 n = 4^{2}$

Simplify the right side.

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

$32 - 2 n = 16$

Solve for $n$ .

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

Subtract $32$ from both sides of the equation.

$- 2 n = 16 - 32$

Subtract $32$ from $16$ .

$- 2 n = - 16$

Divide each term in $- 2 n = - 16$ by $- 2$ and simplify.

Divide each term in $- 2 n = - 16$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{- 16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{- 16}{- 2}$

Divide $n$ by $1$ .

$n = \frac{- 16}{- 2}$

Simplify the right side.

Divide $- 16$ by $- 2$ .

$n = 8$

Solve for n -4=-8+ square root of 32-2n

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