Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $7$ from both sides of the equation.

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

Step 1.2

Subtract $7$ from $216$ .

$3 x^{3} = 209$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Combine and simplify the denominator.

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Step 4.3.1

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

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

Step 4.3.2

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

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

Step 4.3.3

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

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

Step 4.3.4

Add $1$ and $2$ .

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

Step 4.3.5

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

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Step 4.3.5.1

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

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

Step 4.3.5.2

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

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

Step 4.3.5.3

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

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

Step 4.3.5.4

Cancel the common factor of $3$ .

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Step 4.3.5.4.1

Cancel the common factor.

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

Step 4.3.5.4.2

Rewrite the expression.

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

Step 4.3.5.5

Evaluate the exponent.

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

Step 4.4

Simplify the numerator.

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Step 4.4.1

Rewrite ${\sqrt[3]{3}}^{2}$ as $\sqrt[3]{3^{2}}$ .

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

Step 4.4.2

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

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Combine using the product rule for radicals.

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

Step 4.5.2

Multiply $209$ by $9$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.11473316 \dots$