Solve for x -2 square root of x/8=-4

$- 2 \sqrt{\frac{x}{8}} = - 4$

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

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

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{x}{8}}$ as ${(\frac{x}{8})}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${(- 2 {(\frac{x}{8})}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $\frac{x}{8}$ .

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

Combine $- 2$ and $\frac{x^{\frac{1}{2}}}{8^{\frac{1}{2}}}$ .

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

Move the negative in front of the fraction.

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{2 x^{\frac{1}{2}}}{8^{\frac{1}{2}}}$ .

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

Apply the product rule to $\frac{2 x^{\frac{1}{2}}}{8^{\frac{1}{2}}}$ .

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

Apply the product rule to $2 x^{\frac{1}{2}}$ .

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

Simplify the expression.

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

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

Multiply $\frac{2^{2} {(x^{\frac{1}{2}})}^{2}}{{(8^{\frac{1}{2}})}^{2}}$ by $1$ .

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

Simplify the numerator.

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the denominator.

Multiply the exponents in ${(8^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 x$ .

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

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

$\frac{x}{2} = 16$

Solve for $x$ .

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 16$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 16$

Rewrite the expression.

$x = 2 \cdot 16$

Simplify the right side.

Multiply $2$ by $16$ .

$x = 32$

Solve for x -2 square root of x/8=-4

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