Pre-Algebra Examples

$8 x^{2} + 11 + 3 = 0$

Step 1

Add $11$ and $3$ .

$8 x^{2} + 14 = 0$

Step 2

Subtract $14$ from both sides of the equation.

$8 x^{2} = - 14$

Step 3

Divide each term in $8 x^{2} = - 14$ by $8$ and simplify.

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Step 3.1

Divide each term in $8 x^{2} = - 14$ by $8$ .

$\frac{8 x^{2}}{8} = \frac{- 14}{8}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 x^{2}}{8} = \frac{- 14}{8}$

Step 3.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 14}{8}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $- 14$ and $8$ .

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Step 3.3.1.1

Factor $2$ out of $- 14$ .

$x^{2} = \frac{2 (- 7)}{8}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $8$ .

$x^{2} = \frac{2 \cdot - 7}{2 \cdot 4}$

Step 3.3.1.2.2

Cancel the common factor.

$x^{2} = \frac{2 \cdot - 7}{2 \cdot 4}$

Step 3.3.1.2.3

Rewrite the expression.

$x^{2} = \frac{- 7}{4}$

Step 3.3.2

Move the negative in front of the fraction.

$x^{2} = - \frac{7}{4}$

Step 4

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

$x = \pm \sqrt{- \frac{7}{4}}$

Step 5

Simplify $\pm \sqrt{- \frac{7}{4}}$ .

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Step 5.1

Rewrite $- \frac{7}{4}$ as ${(\frac{i}{2})}^{2} \cdot 7$ .

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Step 5.1.1

Rewrite $- 1$ as $i^{2}$ .

$x = \pm \sqrt{i^{2} \frac{7}{4}}$

Step 5.1.2

Factor the perfect power $1^{2}$ out of $7$ .

$x = \pm \sqrt{i^{2} \frac{1^{2} \cdot 7}{4}}$

Step 5.1.3

Factor the perfect power $2^{2}$ out of $4$ .

$x = \pm \sqrt{i^{2} \frac{1^{2} \cdot 7}{2^{2} \cdot 1}}$

Step 5.1.4

Rearrange the fraction $\frac{1^{2} \cdot 7}{2^{2} \cdot 1}$ .

$x = \pm \sqrt{i^{2} ({(\frac{1}{2})}^{2} \cdot 7)}$

Step 5.1.5

Rewrite $i^{2} {(\frac{1}{2})}^{2}$ as ${(\frac{i}{2})}^{2}$ .

$x = \pm \sqrt{{(\frac{i}{2})}^{2} \cdot 7}$

Step 5.2

Pull terms out from under the radical.

$x = \pm \frac{i}{2} \sqrt{7}$

Step 5.3

Combine $\frac{i}{2}$ and $\sqrt{7}$ .

$x = \pm \frac{i \sqrt{7}}{2}$

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.

$x = \frac{i \sqrt{7}}{2}$

Step 6.2

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

$x = - \frac{i \sqrt{7}}{2}$

Step 6.3

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

$x = \frac{i \sqrt{7}}{2}, - \frac{i \sqrt{7}}{2}$