Find All Complex Solutions 4 square root of x+2=-16

$4 \sqrt{x + 2} = - 16$

Step 1

Add $16$ to both sides of the equation.

$4 \sqrt{x + 2} + 16 = 0$

Step 2

Factor $4$ out of $4 \sqrt{x + 2} + 16$ .

Factor $4$ out of $4 \sqrt{x + 2}$ .

$4 (\sqrt{x + 2}) + 16 = 0$

Factor $4$ out of $16$ .

$4 \sqrt{x + 2} + 4 \cdot 4 = 0$

Factor $4$ out of $4 \sqrt{x + 2} + 4 \cdot 4$ .

$4 (\sqrt{x + 2} + 4) = 0$

Step 3

Divide each term in $4 (\sqrt{x + 2} + 4) = 0$ by $4$ and simplify.

Divide each term in $4 (\sqrt{x + 2} + 4) = 0$ by $4$ .

$\frac{4 (\sqrt{x + 2} + 4)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (\sqrt{x + 2} + 4)}{4} = \frac{0}{4}$

Divide $\sqrt{x + 2} + 4$ by $1$ .

$\sqrt{x + 2} + 4 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$\sqrt{x + 2} + 4 = 0$

Step 4

Subtract $4$ from both sides of the equation.

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

Step 5

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

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

Step 6

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$x + 2 = 16$

Step 7

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

Subtract $2$ from both sides of the equation.

$x = 16 - 2$

Subtract $2$ from $16$ .

$x = 14$

Find All Complex Solutions 4 square root of x+2=-16

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