Solve for x fourth root of 4x+4=-2

$\sqrt[4]{4 x + 4} = - 2$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{4 x + 4}}^{4} = {(- 2)}^{4}$

Simplify each side of the equation.

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

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

Simplify the left side.

Simplify ${({(4 x + 4)}^{\frac{1}{4}})}^{4}$ .

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$4 x + 4 = {(- 2)}^{4}$

Simplify the right side.

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

$4 x + 4 = 16$

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$4 x = 16 - 4$

Subtract $4$ from $16$ .

$4 x = 12$

Divide each term in $4 x = 12$ by $4$ and simplify.

Divide each term in $4 x = 12$ by $4$ .

$\frac{4 x}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{12}{4}$

Divide $x$ by $1$ .

$x = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$x = 3$

Exclude the solutions that do not make $\sqrt[4]{4 x + 4} = - 2$ true.

$No solution$