Algebra Examples

$\sqrt[3]{8 x - 8} - 4 = 0$

Step 1

Factor $8$ out of $8 x - 8$ .

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Step 1.1

Factor $8$ out of $8 x$ .

$\sqrt[3]{8 (x) - 8} - 4 = 0$

Step 1.2

Factor $8$ out of $- 8$ .

$\sqrt[3]{8 (x) + 8 (- 1)} - 4 = 0$

Step 1.3

Factor $8$ out of $8 (x) + 8 (- 1)$ .

$\sqrt[3]{8 (x - 1)} - 4 = 0$

Step 2

Rewrite $8 (x - 1)$ as $2^{3} (x + {(- 1)}^{3})$ .

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Step 2.1

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} (x - 1)} - 4 = 0$

Step 2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{2^{3} (x + {(- 1)}^{3})} - 4 = 0$

Step 3

Pull terms out from under the radical.

$2 \sqrt[3]{x + {(- 1)}^{3}} - 4 = 0$

Step 4

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

$2 \sqrt[3]{x - 1} - 4 = 0$

Step 5

Factor $2$ out of $2 \sqrt[3]{x - 1} - 4$ .

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Step 5.1

Factor $2$ out of $2 \sqrt[3]{x - 1}$ .

$2 (\sqrt[3]{x - 1}) - 4 = 0$

Step 5.2

Factor $2$ out of $- 4$ .

$2 \sqrt[3]{x - 1} + 2 \cdot - 2 = 0$

Step 5.3

Factor $2$ out of $2 \sqrt[3]{x - 1} + 2 \cdot - 2$ .

$2 (\sqrt[3]{x - 1} - 2) = 0$

Step 6

Divide each term in $2 (\sqrt[3]{x - 1} - 2) = 0$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 (\sqrt[3]{x - 1} - 2) = 0$ by $2$ .

$\frac{2 (\sqrt[3]{x - 1} - 2)}{2} = \frac{0}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 (\sqrt[3]{x - 1} - 2)}{2} = \frac{0}{2}$

Step 6.2.1.2

Divide $\sqrt[3]{x - 1} - 2$ by $1$ .

$\sqrt[3]{x - 1} - 2 = \frac{0}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $0$ by $2$ .

$\sqrt[3]{x - 1} - 2 = 0$

Step 7

Add $2$ to both sides of the equation.

$\sqrt[3]{x - 1} = 2$

Step 8

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

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

Step 9

Simplify each side of the equation.

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Step 9.1

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

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

Step 9.2

Simplify the left side.

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Step 9.2.1

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

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Step 9.2.1.1

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

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Step 9.2.1.1.1

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

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

Step 9.2.1.1.2

Cancel the common factor of $3$ .

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Step 9.2.1.1.2.1

Cancel the common factor.

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

Step 9.2.1.1.2.2

Rewrite the expression.

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

Step 9.2.1.2

Simplify.

$x - 1 = 2^{3}$

Step 9.3

Simplify the right side.

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Step 9.3.1

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

$x - 1 = 8$

Step 10

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

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Step 10.1

Add $1$ to both sides of the equation.

$x = 8 + 1$

Step 10.2

Add $8$ and $1$ .

$x = 9$