Pre-Algebra Examples

$- y^{2} - 7 = 0$

Step 1

Add $7$ to both sides of the equation.

$- y^{2} = 7$

Step 2

Divide each term in $- y^{2} = 7$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- y^{2} = 7$ by $- 1$ .

$\frac{- y^{2}}{- 1} = \frac{7}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y^{2}}{1} = \frac{7}{- 1}$

Step 2.2.2

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

$y^{2} = \frac{7}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $7$ by $- 1$ .

$y^{2} = - 7$

Step 3

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

$y = \pm \sqrt{- 7}$

Step 4

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

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Step 4.1

Rewrite $- 7$ as $- 1 (7)$ .

$y = \pm \sqrt{- 1 (7)}$

Step 4.2

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$y = \pm \sqrt{- 1} \cdot \sqrt{7}$

Step 4.3

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

$y = \pm i \sqrt{7}$

Step 5

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

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Step 5.1

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

$y = i \sqrt{7}$

Step 5.2

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

$y = - i \sqrt{7}$

Step 5.3

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

$y = i \sqrt{7}, - i \sqrt{7}$