Algebra Examples

$4 x^{3} = 324$

Step 1

Subtract $324$ from both sides of the equation.

$4 x^{3} - 324 = 0$

Step 2

Factor $4$ out of $4 x^{3} - 324$ .

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Step 2.1

Factor $4$ out of $4 x^{3}$ .

$4 (x^{3}) - 324 = 0$

Step 2.2

Factor $4$ out of $- 324$ .

$4 x^{3} + 4 \cdot - 81 = 0$

Step 2.3

Factor $4$ out of $4 x^{3} + 4 \cdot - 81$ .

$4 (x^{3} - 81) = 0$

Step 3

Divide each term in $4 (x^{3} - 81) = 0$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 (x^{3} - 81) = 0$ by $4$ .

$\frac{4 (x^{3} - 81)}{4} = \frac{0}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 (x^{3} - 81)}{4} = \frac{0}{4}$

Step 3.2.1.2

Divide $x^{3} - 81$ by $1$ .

$x^{3} - 81 = \frac{0}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $4$ .

$x^{3} - 81 = 0$

Step 4

Add $81$ to both sides of the equation.

$x^{3} = 81$

Step 5

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

$x = \sqrt[3]{81}$

Step 6

Simplify $\sqrt[3]{81}$ .

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Step 6.1

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 6.1.1

Factor $27$ out of $81$ .

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

Step 6.1.2

Rewrite $27$ as $3^{3}$ .

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

Step 6.2

Pull terms out from under the radical.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.32674871 \dots$