Basic Math Examples

$15 = V \cdot \frac{60}{V} \cdot 0.87 - 4.9 {(\frac{60}{V})}^{2}$

Step 1

Rewrite the equation as $V \cdot \frac{60}{V} \cdot 0.87 - 4.9 {(\frac{60}{V})}^{2} = 15$ .

$V \cdot \frac{60}{V} \cdot 0.87 - 4.9 {(\frac{60}{V})}^{2} = 15$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $V$ .

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Step 2.1.1

Cancel the common factor.

$V \cdot \frac{60}{V} \cdot 0.87 - 4.9 {(\frac{60}{V})}^{2} = 15$

Step 2.1.2

Rewrite the expression.

$60 \cdot 0.87 - 4.9 {(\frac{60}{V})}^{2} = 15$

Step 2.2

Multiply $60$ by $0.87$ .

$52.2 - 4.9 {(\frac{60}{V})}^{2} = 15$

Step 2.3

Apply the product rule to $\frac{60}{V}$ .

$52.2 - 4.9 \frac{60^{2}}{V^{2}} = 15$

Step 2.4

Raise $60$ to the power of $2$ .

$52.2 - 4.9 \frac{3600}{V^{2}} = 15$

Step 2.5

Multiply $- 4.9 \frac{3600}{V^{2}}$ .

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Step 2.5.1

Combine $- 4.9$ and $\frac{3600}{V^{2}}$ .

$52.2 + \frac{- 4.9 \cdot 3600}{V^{2}} = 15$

Step 2.5.2

Multiply $- 4.9$ by $3600$ .

$52.2 + \frac{- 17640}{V^{2}} = 15$

Step 2.6

Move the negative in front of the fraction.

$52.2 - \frac{17640}{V^{2}} = 15$

Step 3

Move all terms not containing $V$ to the right side of the equation.

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Step 3.1

Subtract $52.2$ from both sides of the equation.

$- \frac{17640}{V^{2}} = 15 - 52.2$

Step 3.2

Subtract $52.2$ from $15$ .

$- \frac{17640}{V^{2}} = - 37.2$

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$V^{2}, 1$

Step 4.2

The LCM of one and any expression is the expression.

$V^{2}$

Step 5

Multiply each term in $- \frac{17640}{V^{2}} = - 37.2$ by $V^{2}$ to eliminate the fractions.

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Step 5.1

Multiply each term in $- \frac{17640}{V^{2}} = - 37.2$ by $V^{2}$ .

$- \frac{17640}{V^{2}} V^{2} = - 37.2 V^{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $V^{2}$ .

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Step 5.2.1.1

Move the leading negative in $- \frac{17640}{V^{2}}$ into the numerator.

$\frac{- 17640}{V^{2}} V^{2} = - 37.2 V^{2}$

Step 5.2.1.2

Cancel the common factor.

$\frac{- 17640}{V^{2}} V^{2} = - 37.2 V^{2}$

Step 5.2.1.3

Rewrite the expression.

$- 17640 = - 37.2 V^{2}$

Step 6

Solve the equation.

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Step 6.1

Rewrite the equation as $- 37.2 V^{2} = - 17640$ .

$- 37.2 V^{2} = - 17640$

Step 6.2

Divide each term in $- 37.2 V^{2} = - 17640$ by $- 37.2$ and simplify.

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Step 6.2.1

Divide each term in $- 37.2 V^{2} = - 17640$ by $- 37.2$ .

$\frac{- 37.2 V^{2}}{- 37.2} = \frac{- 17640}{- 37.2}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $- 37.2$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{- 37.2 V^{2}}{- 37.2} = \frac{- 17640}{- 37.2}$

Step 6.2.2.1.2

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

$V^{2} = \frac{- 17640}{- 37.2}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $- 17640$ by $- 37.2$ .

$V^{2} = 474.19354838$

Step 6.3

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

$V = \pm \sqrt{474.19354838}$

Step 6.4

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

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Step 6.4.1

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

$V = \sqrt{474.19354838}$

Step 6.4.2

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

$V = - \sqrt{474.19354838}$

Step 6.4.3

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

$V = \sqrt{474.19354838}, - \sqrt{474.19354838}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$V = \sqrt{474.19354838}, - \sqrt{474.19354838}$

Decimal Form:

$V = 21.77598558 \dots, - 21.77598558 \dots$