Pre-Algebra Examples

${(6 x + 20)}^{2} = 48$

Step 1

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

$6 x + 20 = \pm \sqrt{48}$

Step 2

Simplify $\pm \sqrt{48}$ .

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Step 2.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 2.1.1

Factor $16$ out of $48$ .

$6 x + 20 = \pm \sqrt{16 (3)}$

Step 2.1.2

Rewrite $16$ as $4^{2}$ .

$6 x + 20 = \pm \sqrt{4^{2} \cdot 3}$

Step 2.2

Pull terms out from under the radical.

$6 x + 20 = \pm 4 \sqrt{3}$

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.

$6 x + 20 = 4 \sqrt{3}$

Step 3.2

Subtract $20$ from both sides of the equation.

$6 x = 4 \sqrt{3} - 20$

Step 3.3

Divide each term in $6 x = 4 \sqrt{3} - 20$ by $6$ and simplify.

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Step 3.3.1

Divide each term in $6 x = 4 \sqrt{3} - 20$ by $6$ .

$\frac{6 x}{6} = \frac{4 \sqrt{3}}{6} + \frac{- 20}{6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{4 \sqrt{3}}{6} + \frac{- 20}{6}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{4 \sqrt{3}}{6} + \frac{- 20}{6}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Simplify each term.

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Step 3.3.3.1.1

Cancel the common factor of $4$ and $6$ .

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Step 3.3.3.1.1.1

Factor $2$ out of $4 \sqrt{3}$ .

$x = \frac{2 (2 \sqrt{3})}{6} + \frac{- 20}{6}$

Step 3.3.3.1.1.2

Cancel the common factors.

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Step 3.3.3.1.1.2.1

Factor $2$ out of $6$ .

$x = \frac{2 (2 \sqrt{3})}{2 (3)} + \frac{- 20}{6}$

Step 3.3.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 (2 \sqrt{3})}{2 \cdot 3} + \frac{- 20}{6}$

Step 3.3.3.1.1.2.3

Rewrite the expression.

$x = \frac{2 \sqrt{3}}{3} + \frac{- 20}{6}$

Step 3.3.3.1.2

Cancel the common factor of $- 20$ and $6$ .

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Step 3.3.3.1.2.1

Factor $2$ out of $- 20$ .

$x = \frac{2 \sqrt{3}}{3} + \frac{2 (- 10)}{6}$

Step 3.3.3.1.2.2

Cancel the common factors.

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Step 3.3.3.1.2.2.1

Factor $2$ out of $6$ .

$x = \frac{2 \sqrt{3}}{3} + \frac{2 \cdot - 10}{2 \cdot 3}$

Step 3.3.3.1.2.2.2

Cancel the common factor.

$x = \frac{2 \sqrt{3}}{3} + \frac{2 \cdot - 10}{2 \cdot 3}$

Step 3.3.3.1.2.2.3

Rewrite the expression.

$x = \frac{2 \sqrt{3}}{3} + \frac{- 10}{3}$

Step 3.3.3.1.3

Move the negative in front of the fraction.

$x = \frac{2 \sqrt{3}}{3} - \frac{10}{3}$

Step 3.4

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

$6 x + 20 = - 4 \sqrt{3}$

Step 3.5

Subtract $20$ from both sides of the equation.

$6 x = - 4 \sqrt{3} - 20$

Step 3.6

Divide each term in $6 x = - 4 \sqrt{3} - 20$ by $6$ and simplify.

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Step 3.6.1

Divide each term in $6 x = - 4 \sqrt{3} - 20$ by $6$ .

$\frac{6 x}{6} = \frac{- 4 \sqrt{3}}{6} + \frac{- 20}{6}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $6$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 4 \sqrt{3}}{6} + \frac{- 20}{6}$

Step 3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4 \sqrt{3}}{6} + \frac{- 20}{6}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Simplify each term.

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Step 3.6.3.1.1

Cancel the common factor of $- 4$ and $6$ .

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Step 3.6.3.1.1.1

Factor $2$ out of $- 4 \sqrt{3}$ .

$x = \frac{2 (- 2 \sqrt{3})}{6} + \frac{- 20}{6}$

Step 3.6.3.1.1.2

Cancel the common factors.

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Step 3.6.3.1.1.2.1

Factor $2$ out of $6$ .

$x = \frac{2 (- 2 \sqrt{3})}{2 (3)} + \frac{- 20}{6}$

Step 3.6.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 (- 2 \sqrt{3})}{2 \cdot 3} + \frac{- 20}{6}$

Step 3.6.3.1.1.2.3

Rewrite the expression.

$x = \frac{- 2 \sqrt{3}}{3} + \frac{- 20}{6}$

Step 3.6.3.1.2

Move the negative in front of the fraction.

$x = - \frac{2 \sqrt{3}}{3} + \frac{- 20}{6}$

Step 3.6.3.1.3

Cancel the common factor of $- 20$ and $6$ .

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Step 3.6.3.1.3.1

Factor $2$ out of $- 20$ .

$x = - \frac{2 \sqrt{3}}{3} + \frac{2 (- 10)}{6}$

Step 3.6.3.1.3.2

Cancel the common factors.

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Step 3.6.3.1.3.2.1

Factor $2$ out of $6$ .

$x = - \frac{2 \sqrt{3}}{3} + \frac{2 \cdot - 10}{2 \cdot 3}$

Step 3.6.3.1.3.2.2

Cancel the common factor.

$x = - \frac{2 \sqrt{3}}{3} + \frac{2 \cdot - 10}{2 \cdot 3}$

Step 3.6.3.1.3.2.3

Rewrite the expression.

$x = - \frac{2 \sqrt{3}}{3} + \frac{- 10}{3}$

Step 3.6.3.1.4

Move the negative in front of the fraction.

$x = - \frac{2 \sqrt{3}}{3} - \frac{10}{3}$

Step 3.7

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

$x = \frac{2 \sqrt{3}}{3} - \frac{10}{3}, - \frac{2 \sqrt{3}}{3} - \frac{10}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2 \sqrt{3}}{3} - \frac{10}{3}, - \frac{2 \sqrt{3}}{3} - \frac{10}{3}$

Decimal Form:

$x = - 2.17863279 \dots, - 4.48803387 \dots$