Basic Math Examples

2.56 = \frac{v^{2}}{9.81 (0.79)}

$2.56 = \frac{v^{2}}{9.81 (0.79)}$

Step 1

Rewrite the equation as

\frac{v^{2}}{9.81 (0.79)} = 2.56

$\frac{v^{2}}{9.81 (0.79)} = 2.56$ .

\frac{v^{2}}{9.81 (0.79)} = 2.56

$\frac{v^{2}}{9.81 (0.79)} = 2.56$

Step 2

Multiply both sides of the equation by

9.81 (0.79)

$9.81 (0.79)$ .

9.81 \cdot 0.79 \frac{v^{2}}{9.81 \cdot 0.79} = 9.81 (0.79) \cdot 2.56

$9.81 \cdot 0.79 \frac{v^{2}}{9.81 \cdot 0.79} = 9.81 (0.79) \cdot 2.56$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify

9.81 \cdot 0.79 \frac{v^{2}}{9.81 \cdot 0.79}

$9.81 \cdot 0.79 \frac{v^{2}}{9.81 \cdot 0.79}$ .

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Step 3.1.1.1

Multiply.

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Step 3.1.1.1.1

Multiply

9.81

$9.81$ by

0.79

$0.79$ .

7.7499 \frac{v^{2}}{9.81 \cdot 0.79} = 9.81 (0.79) \cdot 2.56

$7.7499 \frac{v^{2}}{9.81 \cdot 0.79} = 9.81 (0.79) \cdot 2.56$

Step 3.1.1.1.2

Multiply

9.81

$9.81$ by

0.79

$0.79$ .

7.7499 \frac{v^{2}}{7.7499} = 9.81 (0.79) \cdot 2.56

$7.7499 \frac{v^{2}}{7.7499} = 9.81 (0.79) \cdot 2.56$

7.7499 \frac{v^{2}}{7.7499} = 9.81 (0.79) \cdot 2.56

$7.7499 \frac{v^{2}}{7.7499} = 9.81 (0.79) \cdot 2.56$

Step 3.1.1.2

Cancel the common factor of

7.7499

$7.7499$ .

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Step 3.1.1.2.1

Cancel the common factor.

$7.7499 \frac{v^{2}}{7.7499} = 9.81 (0.79) \cdot 2.56$

Step 3.1.1.2.2

Rewrite the expression.

$v^{2} = 9.81 (0.79) \cdot 2.56$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply

$9.81 (0.79) \cdot 2.56$ .

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Step 3.2.1.1

Multiply

$9.81$ by

$0.79$ .

$v^{2} = 7.7499 \cdot 2.56$

Step 3.2.1.2

Multiply

$7.7499$ by

$2.56$ .

$v^{2} = 19.839744$

Step 4

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

$v = \pm \sqrt{19.839744}$

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.

$v = \sqrt{19.839744}$

Step 5.2

Next, use the negative value of the

$\pm$ to find the second solution.

$v = - \sqrt{19.839744}$

Step 5.3

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

$v = \sqrt{19.839744}, - \sqrt{19.839744}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = \sqrt{19.839744}, - \sqrt{19.839744}$

Decimal Form:

$v = 4.45418275 \dots, - 4.45418275 \dots$