Finite Math Examples

${(3 k + 4)}^{2} = 64$

Step 1

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

$3 k + 4 = \pm \sqrt{64}$

Step 2

Simplify $\pm \sqrt{64}$ .

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$3 k + 4 = \pm \sqrt{8^{2}}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$3 k + 4 = \pm 8$

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.

$3 k + 4 = 8$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$3 k = 8 - 4$

Step 3.2.2

Subtract $4$ from $8$ .

$3 k = 4$

Step 3.3

Divide each term in $3 k = 4$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 k = 4$ by $3$ .

$\frac{3 k}{3} = \frac{4}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 k}{3} = \frac{4}{3}$

Step 3.3.2.1.2

Divide $k$ by $1$ .

$k = \frac{4}{3}$

Step 3.4

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

$3 k + 4 = - 8$

Step 3.5

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

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Step 3.5.1

Subtract $4$ from both sides of the equation.

$3 k = - 8 - 4$

Step 3.5.2

Subtract $4$ from $- 8$ .

$3 k = - 12$

Step 3.6

Divide each term in $3 k = - 12$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 k = - 12$ by $3$ .

$\frac{3 k}{3} = \frac{- 12}{3}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 k}{3} = \frac{- 12}{3}$

Step 3.6.2.1.2

Divide $k$ by $1$ .

$k = \frac{- 12}{3}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $- 12$ by $3$ .

$k = - 4$

Step 3.7

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

$k = \frac{4}{3}, - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{4}{3}, - 4$

Decimal Form:

$k = 1.\overline{3}, - 4$

Mixed Number Form:

$k = 1 \frac{1}{3}, - 4$