Solve for x cube root of 486-27x^3=3x

$\sqrt[3]{486 - 27 x^{3}} = 3 x$

Step 1

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

${\sqrt[3]{486 - 27 x^{3}}}^{3} = {(3 x)}^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{486 - 27 x^{3}}$ as ${(486 - 27 x^{3})}^{\frac{1}{3}}$ .

${({(486 - 27 x^{3})}^{\frac{1}{3}})}^{3} = {(3 x)}^{3}$

Simplify the left side.

Simplify ${({(486 - 27 x^{3})}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(486 - 27 x^{3})}^{\frac{1}{3}})}^{3}$ .

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

${(486 - 27 x^{3})}^{\frac{1}{3} \cdot 3} = {(3 x)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(486 - 27 x^{3})}^{\frac{1}{3} \cdot 3} = {(3 x)}^{3}$

Rewrite the expression.

${(486 - 27 x^{3})}^{1} = {(3 x)}^{3}$

Simplify.

$486 - 27 x^{3} = {(3 x)}^{3}$

Simplify the right side.

Simplify ${(3 x)}^{3}$ .

Apply the product rule to $3 x$ .

$486 - 27 x^{3} = 3^{3} x^{3}$

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

$486 - 27 x^{3} = 27 x^{3}$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $27 x^{3}$ from both sides of the equation.

$486 - 27 x^{3} - 27 x^{3} = 0$

Subtract $27 x^{3}$ from $- 27 x^{3}$ .

$486 - 54 x^{3} = 0$

Subtract $486$ from both sides of the equation.

$- 54 x^{3} = - 486$

Add $486$ to both sides of the equation.

$- 54 x^{3} + 486 = 0$

Factor $- 54$ out of $- 54 x^{3} + 486$ .

Factor $- 54$ out of $- 54 x^{3}$ .

$- 54 x^{3} + 486 = 0$

Factor $- 54$ out of $486$ .

$- 54 x^{3} - 54 \cdot - 9 = 0$

Factor $- 54$ out of $- 54 (x^{3}) - 54 (- 9)$ .

$- 54 (x^{3} - 9) = 0$

Divide each term in $- 54 (x^{3} - 9) = 0$ by $- 54$ and simplify.

Divide each term in $- 54 (x^{3} - 9) = 0$ by $- 54$ .

$\frac{- 54 (x^{3} - 9)}{- 54} = \frac{0}{- 54}$

Simplify the left side.

Cancel the common factor of $- 54$ .

Cancel the common factor.

$\frac{- 54 (x^{3} - 9)}{- 54} = \frac{0}{- 54}$

Divide $x^{3} - 9$ by $1$ .

$x^{3} - 9 = \frac{0}{- 54}$

Simplify the right side.

Divide $0$ by $- 54$ .

$x^{3} - 9 = 0$

Add $9$ to both sides of the equation.

$x^{3} = 9$

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[3]{9}$

Decimal Form:

$x = 2.08008382 \dots$

Solve for x cube root of 486-27x^3=3x

Related Questions

Support LCMGCF.com by disabling your adblocker.