Basic Math Examples

$1320 = \frac{1}{2} \cdot 60 \cdot y^{2}$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot 60 \cdot y^{2} = 1320$ .

$\frac{1}{2} \cdot 60 \cdot y^{2} = 1320$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $60$ .

$\frac{1}{2} \cdot (2 (30)) \cdot y^{2} = 1320$

Step 2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 30) \cdot y^{2} = 1320$

Step 2.3

Rewrite the expression.

$30 \cdot y^{2} = 1320$

Step 3

Divide each term in $30 \cdot y^{2} = 1320$ by $30$ and simplify.

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Step 3.1

Divide each term in $30 \cdot y^{2} = 1320$ by $30$ .

$\frac{30 \cdot y^{2}}{30} = \frac{1320}{30}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $30$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{30 \cdot y^{2}}{30} = \frac{1320}{30}$

Step 3.2.1.2

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

$y^{2} = \frac{1320}{30}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $1320$ by $30$ .

$y^{2} = 44$

Step 4

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

$y = \pm \sqrt{44}$

Step 5

Simplify $\pm \sqrt{44}$ .

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Step 5.1

Rewrite $44$ as $2^{2} \cdot 11$ .

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Step 5.1.1

Factor $4$ out of $44$ .

$y = \pm \sqrt{4 (11)}$

Step 5.1.2

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

$y = \pm \sqrt{2^{2} \cdot 11}$

Step 5.2

Pull terms out from under the radical.

$y = \pm 2 \sqrt{11}$

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.

$y = 2 \sqrt{11}$

Step 6.2

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

$y = - 2 \sqrt{11}$

Step 6.3

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

$y = 2 \sqrt{11}, - 2 \sqrt{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = 2 \sqrt{11}, - 2 \sqrt{11}$

Decimal Form:

$y = 6.63324958 \dots, - 6.63324958 \dots$