Algebra Examples

$\sqrt[3]{{(3 x + 8)}^{2}} = 1$

Step 1

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

${\sqrt[3]{{(3 x + 8)}^{2}}}^{3} = 1^{3}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{{(3 x + 8)}^{2}}$ as ${(3 x + 8)}^{\frac{2}{3}}$ .

${({(3 x + 8)}^{\frac{2}{3}})}^{3} = 1^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply the exponents in ${({(3 x + 8)}^{\frac{2}{3}})}^{3}$ .

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Step 2.2.1.1

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

${(3 x + 8)}^{\frac{2}{3} \cdot 3} = 1^{3}$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Cancel the common factor.

${(3 x + 8)}^{\frac{2}{3} \cdot 3} = 1^{3}$

Step 2.2.1.2.2

Rewrite the expression.

${(3 x + 8)}^{2} = 1^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

One to any power is one.

${(3 x + 8)}^{2} = 1$

Step 3

Solve for $x$ .

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Step 3.1

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

$3 x + 8 = \pm \sqrt{1}$

Step 3.2

Any root of $1$ is $1$ .

$3 x + 8 = \pm 1$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$3 x + 8 = 1$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $8$ from both sides of the equation.

$3 x = 1 - 8$

Step 3.3.2.2

Subtract $8$ from $1$ .

$3 x = - 7$

Step 3.3.3

Divide each term in $3 x = - 7$ by $3$ and simplify.

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Step 3.3.3.1

Divide each term in $3 x = - 7$ by $3$ .

$\frac{3 x}{3} = \frac{- 7}{3}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 7}{3}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{3}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{3}$

Step 3.3.4

Next, use the negative value of the $\pm$ to find the second solution.

$3 x + 8 = - 1$

Step 3.3.5

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

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Step 3.3.5.1

Subtract $8$ from both sides of the equation.

$3 x = - 1 - 8$

Step 3.3.5.2

Subtract $8$ from $- 1$ .

$3 x = - 9$

Step 3.3.6

Divide each term in $3 x = - 9$ by $3$ and simplify.

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Step 3.3.6.1

Divide each term in $3 x = - 9$ by $3$ .

$\frac{3 x}{3} = \frac{- 9}{3}$

Step 3.3.6.2

Simplify the left side.

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Step 3.3.6.2.1

Cancel the common factor of $3$ .

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Step 3.3.6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 9}{3}$

Step 3.3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{3}$

Step 3.3.6.3

Simplify the right side.

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Step 3.3.6.3.1

Divide $- 9$ by $3$ .

$x = - 3$

Step 3.3.7

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \frac{7}{3}, - 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{3}, - 3$

Decimal Form:

$x = - 2.\overline{3}, - 3$

Mixed Number Form:

$x = - 2 \frac{1}{3}, - 3$