Solve for x 2 cube root of x=4 cube root of x+7

$2 \sqrt[3]{x} = 4 \sqrt[3]{x} + 7$

Solve for $\sqrt[3]{x}$ .

Move all terms containing $\sqrt[3]{x}$ to the left side of the equation.

Subtract $4 \sqrt[3]{x}$ from both sides of the equation.

$2 \sqrt[3]{x} - 4 \sqrt[3]{x} = 7$

Subtract $4 \sqrt[3]{x}$ from $2 \sqrt[3]{x}$ .

$- 2 \sqrt[3]{x} = 7$

Divide each term in $- 2 \sqrt[3]{x} = 7$ by $- 2$ and simplify.

Divide each term in $- 2 \sqrt[3]{x} = 7$ by $- 2$ .

$\frac{- 2 \sqrt[3]{x}}{- 2} = \frac{7}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 \sqrt[3]{x}}{- 2} = \frac{7}{- 2}$

Divide $\sqrt[3]{x}$ by $1$ .

$\sqrt[3]{x} = \frac{7}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$\sqrt[3]{x} = - \frac{7}{2}$

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

${\sqrt[3]{x}}^{3} = {(- \frac{7}{2})}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

${(x^{\frac{1}{3}})}^{3} = {(- \frac{7}{2})}^{3}$

Simplify the left side.

Simplify ${(x^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${(x^{\frac{1}{3}})}^{3}$ .

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

$x^{\frac{1}{3} \cdot 3} = {(- \frac{7}{2})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = {(- \frac{7}{2})}^{3}$

Rewrite the expression.

$x^{1} = {(- \frac{7}{2})}^{3}$

Simplify.

$x = {(- \frac{7}{2})}^{3}$

Simplify the right side.

Simplify ${(- \frac{7}{2})}^{3}$ .

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

Apply the product rule to $- \frac{7}{2}$ .

$x = {(- 1)}^{3} {(\frac{7}{2})}^{3}$

Apply the product rule to $\frac{7}{2}$ .

$x = {(- 1)}^{3} \frac{7^{3}}{2^{3}}$

Raise $- 1$ to the power of $3$ .

$x = - \frac{7^{3}}{2^{3}}$

Raise $7$ to the power of $3$ .

$x = - \frac{343}{2^{3}}$

Raise $2$ to the power of $3$ .

$x = - \frac{343}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{343}{8}$

Decimal Form:

$x = - 42.875$

Mixed Number Form:

$x = - 42 \frac{7}{8}$

Solve for x 2 cube root of x=4 cube root of x+7

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