Basic Math Examples

45 \cdot (\frac{1}{2} \cdot 3.2) - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot (\frac{1}{2} \cdot 3.2) = 0

$45 \cdot (\frac{1}{2} \cdot 3.2) - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot (\frac{1}{2} \cdot 3.2) = 0$

Step 1

Simplify

45 \cdot \frac{1}{2} \cdot 3.2 - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2

$45 \cdot \frac{1}{2} \cdot 3.2 - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine

45

$45$ and

\frac{1}{2}

$\frac{1}{2}$ .

\frac{45}{2} \cdot 3.2 - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0

$\frac{45}{2} \cdot 3.2 - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0$

Step 1.1.2

Multiply

\frac{45}{2} \cdot 3.2

$\frac{45}{2} \cdot 3.2$ .

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Step 1.1.2.1

Combine

\frac{45}{2}

$\frac{45}{2}$ and

3.2

$3.2$ .

\frac{45 \cdot 3.2}{2} - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0

$\frac{45 \cdot 3.2}{2} - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0$

Step 1.1.2.2

Multiply

45

$45$ by

3.2

$3.2$ .

\frac{144}{2} - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0

$\frac{144}{2} - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0$

\frac{144}{2} - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0

$\frac{144}{2} - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0$

Step 1.1.3

Divide

144

$144$ by

2

$2$ .

72 - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0

$72 - 25 \cdot 9.81 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0$

Step 1.1.4

Multiply

- 25

$- 25$ by

9.81

$9.81$ .

72 - 245.25 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0

$72 - 245.25 \cdot b - 35 \cdot 9.81 \cdot \frac{1}{2} \cdot 3.2 = 0$

Step 1.1.5

Multiply

- 35

$- 35$ by

9.81

$9.81$ .

72 - 245.25 b - 343.35 \cdot \frac{1}{2} \cdot 3.2 = 0

$72 - 245.25 b - 343.35 \cdot \frac{1}{2} \cdot 3.2 = 0$

Step 1.1.6

Combine

- 343.35

$- 343.35$ and

\frac{1}{2}

$\frac{1}{2}$ .

72 - 245.25 b + \frac{- 343.35}{2} \cdot 3.2 = 0

$72 - 245.25 b + \frac{- 343.35}{2} \cdot 3.2 = 0$

Step 1.1.7

Divide

- 343.35

$- 343.35$ by

2

$2$ .

72 - 245.25 b - 171.675 \cdot 3.2 = 0

$72 - 245.25 b - 171.675 \cdot 3.2 = 0$

Step 1.1.8

Multiply

- 171.675

$- 171.675$ by

3.2

$3.2$ .

72 - 245.25 b - 549.36 = 0

$72 - 245.25 b - 549.36 = 0$

72 - 245.25 b - 549.36 = 0

$72 - 245.25 b - 549.36 = 0$

Step 1.2

Subtract

549.36

$549.36$ from

72

$72$ .

- 245.25 b - 477.36 = 0

$- 245.25 b - 477.36 = 0$

- 245.25 b - 477.36 = 0

$- 245.25 b - 477.36 = 0$

Step 2

Add

477.36

$477.36$ to both sides of the equation.

- 245.25 b = 477.36

$- 245.25 b = 477.36$

Step 3

Divide each term in

- 245.25 b = 477.36

$- 245.25 b = 477.36$ by

- 245.25

$- 245.25$ and simplify.

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Step 3.1

Divide each term in

- 245.25 b = 477.36

$- 245.25 b = 477.36$ by

- 245.25

$- 245.25$ .

\frac{- 245.25 b}{- 245.25} = \frac{477.36}{- 245.25}

$\frac{- 245.25 b}{- 245.25} = \frac{477.36}{- 245.25}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

- 245.25

$- 245.25$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{- 245.25 b}{- 245.25} = \frac{477.36}{- 245.25}

$\frac{- 245.25 b}{- 245.25} = \frac{477.36}{- 245.25}$

Step 3.2.1.2

Divide

b

$b$ by

1

$1$ .

b = \frac{477.36}{- 245.25}

$b = \frac{477.36}{- 245.25}$

b = \frac{477.36}{- 245.25}

$b = \frac{477.36}{- 245.25}$

b = \frac{477.36}{- 245.25}

$b = \frac{477.36}{- 245.25}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide

477.36

$477.36$ by

- 245.25

$- 245.25$ .

b = - 1.94642201

$b = - 1.94642201$

b = - 1.94642201

$b = - 1.94642201$

b = - 1.94642201

$b = - 1.94642201$