Solve for x 3x^3+7=216

$3 x^{3} + 7 = 216$

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

Subtract $7$ from both sides of the equation.

$3 x^{3} = 216 - 7$

Subtract $7$ from $216$ .

$3 x^{3} = 209$

Divide each term in $3 x^{3} = 209$ by $3$ and simplify.

Divide each term in $3 x^{3} = 209$ by $3$ .

$\frac{3 x^{3}}{3} = \frac{209}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{3}}{3} = \frac{209}{3}$

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

$x^{3} = \frac{209}{3}$

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

$x = \sqrt[3]{\frac{209}{3}}$

Simplify $\sqrt[3]{\frac{209}{3}}$ .

Rewrite $\sqrt[3]{\frac{209}{3}}$ as $\frac{\sqrt[3]{209}}{\sqrt[3]{3}}$ .

$x = \frac{\sqrt[3]{209}}{\sqrt[3]{3}}$

Multiply $\frac{\sqrt[3]{209}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$x = \frac{\sqrt[3]{209}}{\sqrt[3]{3}} \cdot \frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{209}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{\sqrt[3]{3} {\sqrt[3]{3}}^{2}}$

Raise $\sqrt[3]{3}$ to the power of $1$ .

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1} {\sqrt[3]{3}}^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1 + 2}}$

Add $1$ and $2$ .

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{3}}$

Rewrite ${\sqrt[3]{3}}^{3}$ as $3$ .

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

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{{(3^{\frac{1}{3}})}^{3}}$

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

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{3^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Rewrite the expression.

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{3^{1}}$

Evaluate the exponent.

$x = \frac{\sqrt[3]{209} {\sqrt[3]{3}}^{2}}{3}$

Simplify the numerator.

Rewrite ${\sqrt[3]{3}}^{2}$ as ${(3^{2})}^{\frac{1}{3}}$ .

$x = \frac{\sqrt[3]{209} \sqrt[3]{3^{2}}}{3}$

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

$x = \frac{\sqrt[3]{209} \sqrt[3]{9}}{3}$

Simplify the numerator.

Combine using the product rule for radicals.

$x = \frac{\sqrt[3]{209 \cdot 9}}{3}$

Multiply $209$ by $9$ .

$x = \frac{\sqrt[3]{1881}}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt[3]{1881}}{3}$

Decimal Form:

$x = 4.11473316 \dots$

Solve for x 3x^3+7=216

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