Pre-Algebra Examples

$- {(2 x + 6)}^{2} + 14 = 30$

Step 1

Subtract $14$ from both sides of the equation.

$- {(2 x + 6)}^{2} = 30 - 14$

Step 2

Subtract $14$ from $30$ .

$- {(2 x + 6)}^{2} = 16$

Step 3

Divide each term in $- {(2 x + 6)}^{2} = 16$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- {(2 x + 6)}^{2} = 16$ by $- 1$ .

$\frac{- {(2 x + 6)}^{2}}{- 1} = \frac{16}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{{(2 x + 6)}^{2}}{1} = \frac{16}{- 1}$

Step 3.2.2

Divide ${(2 x + 6)}^{2}$ by $1$ .

${(2 x + 6)}^{2} = \frac{16}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $16$ by $- 1$ .

${(2 x + 6)}^{2} = - 16$

Step 4

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

$2 x + 6 = \pm \sqrt{- 16}$

Step 5

Simplify $\pm \sqrt{- 16}$ .

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Step 5.1

Rewrite $- 16$ as $- 1 (16)$ .

$2 x + 6 = \pm \sqrt{- 1 (16)}$

Step 5.2

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$2 x + 6 = \pm \sqrt{- 1} \cdot \sqrt{16}$

Step 5.3

Rewrite $\sqrt{- 1}$ as $i$ .

$2 x + 6 = \pm i \cdot \sqrt{16}$

Step 5.4

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

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

Step 5.5

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

$2 x + 6 = \pm i \cdot 4$

Step 5.6

Move $4$ to the left of $i$ .

$2 x + 6 = \pm 4 i$

Step 6

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

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Step 6.1

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

$2 x + 6 = 4 i$

Step 6.2

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

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Step 6.2.1

Subtract $6$ from both sides of the equation.

$2 x = 4 i - 6$

Step 6.2.2

Reorder $4 i$ and $- 6$ .

$2 x = - 6 + 4 i$

Step 6.3

Divide each term in $2 x = - 6 + 4 i$ by $2$ and simplify.

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Step 6.3.1

Divide each term in $2 x = - 6 + 4 i$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2} + \frac{4 i}{2}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $2$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2} + \frac{4 i}{2}$

Step 6.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{2} + \frac{4 i}{2}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Simplify each term.

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Step 6.3.3.1.1

Divide $- 6$ by $2$ .

$x = - 3 + \frac{4 i}{2}$

Step 6.3.3.1.2

Cancel the common factor of $4$ and $2$ .

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Step 6.3.3.1.2.1

Factor $2$ out of $4 i$ .

$x = - 3 + \frac{2 (2 i)}{2}$

Step 6.3.3.1.2.2

Cancel the common factors.

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Step 6.3.3.1.2.2.1

Factor $2$ out of $2$ .

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

Step 6.3.3.1.2.2.2

Cancel the common factor.

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

Step 6.3.3.1.2.2.3

Rewrite the expression.

$x = - 3 + \frac{2 i}{1}$

Step 6.3.3.1.2.2.4

Divide $2 i$ by $1$ .

$x = - 3 + 2 i$

Step 6.4

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

$2 x + 6 = - 4 i$

Step 6.5

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

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Step 6.5.1

Subtract $6$ from both sides of the equation.

$2 x = - 4 i - 6$

Step 6.5.2

Reorder $- 4 i$ and $- 6$ .

$2 x = - 6 - 4 i$

Step 6.6

Divide each term in $2 x = - 6 - 4 i$ by $2$ and simplify.

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Step 6.6.1

Divide each term in $2 x = - 6 - 4 i$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2} + \frac{- 4 i}{2}$

Step 6.6.2

Simplify the left side.

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Step 6.6.2.1

Cancel the common factor of $2$ .

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Step 6.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2} + \frac{- 4 i}{2}$

Step 6.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{2} + \frac{- 4 i}{2}$

Step 6.6.3

Simplify the right side.

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Step 6.6.3.1

Simplify each term.

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Step 6.6.3.1.1

Divide $- 6$ by $2$ .

$x = - 3 + \frac{- 4 i}{2}$

Step 6.6.3.1.2

Cancel the common factor of $- 4$ and $2$ .

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Step 6.6.3.1.2.1

Factor $2$ out of $- 4 i$ .

$x = - 3 + \frac{2 (- 2 i)}{2}$

Step 6.6.3.1.2.2

Cancel the common factors.

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Step 6.6.3.1.2.2.1

Factor $2$ out of $2$ .

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

Step 6.6.3.1.2.2.2

Cancel the common factor.

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

Step 6.6.3.1.2.2.3

Rewrite the expression.

$x = - 3 + \frac{- 2 i}{1}$

Step 6.6.3.1.2.2.4

Divide $- 2 i$ by $1$ .

$x = - 3 - 2 i$

Step 6.7

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

$x = - 3 + 2 i, - 3 - 2 i$