Pre-Algebra Examples

$x^{2} + 768 = 0$

Step 1

Subtract $768$ from both sides of the equation.

$x^{2} = - 768$

Step 2

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

$x = \pm \sqrt{- 768}$

Step 3

Simplify $\pm \sqrt{- 768}$ .

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Step 3.1

Rewrite $- 768$ as $- 1 (768)$ .

$x = \pm \sqrt{- 1 (768)}$

Step 3.2

Rewrite $\sqrt{- 1 (768)}$ as $\sqrt{- 1} \cdot \sqrt{768}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{768}$

Step 3.3

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

$x = \pm i \cdot \sqrt{768}$

Step 3.4

Rewrite $768$ as $16^{2} \cdot 3$ .

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Step 3.4.1

Factor $256$ out of $768$ .

$x = \pm i \cdot \sqrt{256 (3)}$

Step 3.4.2

Rewrite $256$ as $16^{2}$ .

$x = \pm i \cdot \sqrt{16^{2} \cdot 3}$

Step 3.5

Pull terms out from under the radical.

$x = \pm i \cdot (16 \sqrt{3})$

Step 3.6

Move $16$ to the left of $i$ .

$x = \pm 16 i \sqrt{3}$

Step 4

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

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Step 4.1

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

$x = 16 i \sqrt{3}$

Step 4.2

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

$x = - 16 i \sqrt{3}$

Step 4.3

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

$x = 16 i \sqrt{3}, - 16 i \sqrt{3}$