Algebra Examples

$4 {(x + 1)}^{4} = 68$

Step 1

Divide each term in $4 {(x + 1)}^{4} = 68$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 {(x + 1)}^{4} = 68$ by $4$ .

$\frac{4 {(x + 1)}^{4}}{4} = \frac{68}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 {(x + 1)}^{4}}{4} = \frac{68}{4}$

Step 1.2.1.2

Divide ${(x + 1)}^{4}$ by $1$ .

${(x + 1)}^{4} = \frac{68}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $68$ by $4$ .

${(x + 1)}^{4} = 17$

Step 2

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

$x + 1 = \pm \sqrt[4]{17}$

Step 3

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

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Step 3.1

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

$x + 1 = \sqrt[4]{17}$

Step 3.2

Subtract $1$ from both sides of the equation.

$x = \sqrt[4]{17} - 1$

Step 3.3

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

$x + 1 = - \sqrt[4]{17}$

Step 3.4

Subtract $1$ from both sides of the equation.

$x = - \sqrt[4]{17} - 1$

Step 3.5

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

$x = \sqrt[4]{17} - 1, - \sqrt[4]{17} - 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[4]{17} - 1, - \sqrt[4]{17} - 1$

Decimal Form:

$x = 1.03054318 \dots, - 3.03054318 \dots$