Basic Math Examples

$4 y^{2} + 20 = 0$

Step 1

Subtract $20$ from both sides of the equation.

$4 y^{2} = - 20$

Step 2

Divide each term in $4 y^{2} = - 20$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y^{2} = - 20$ by $4$ .

$\frac{4 y^{2}}{4} = \frac{- 20}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y^{2}}{4} = \frac{- 20}{4}$

Step 2.2.1.2

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

$y^{2} = \frac{- 20}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 20$ by $4$ .

$y^{2} = - 5$

Step 3

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

$y = \pm \sqrt{- 5}$

Step 4

Simplify $\pm \sqrt{- 5}$ .

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Step 4.1

Rewrite $- 5$ as $- 1 (5)$ .

$y = \pm \sqrt{- 1 (5)}$

Step 4.2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$y = \pm \sqrt{- 1} \cdot \sqrt{5}$

Step 4.3

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

$y = \pm i \sqrt{5}$

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.

$y = i \sqrt{5}$

Step 5.2

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

$y = - i \sqrt{5}$

Step 5.3

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

$y = i \sqrt{5}, - i \sqrt{5}$