Finite Math Examples

$\frac{- (- 128) - v ({(- 128)}^{2} - 4 \cdot 16 \cdot 240)}{2 \cdot 16}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $- 128$ .

$\frac{128 - v ({(- 128)}^{2} - 4 \cdot 16 \cdot 240)}{2 \cdot 16}$

Step 1.2

Simplify each term.

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Step 1.2.1

Raise $- 128$ to the power of $2$ .

$\frac{128 - v (16384 - 4 \cdot 16 \cdot 240)}{2 \cdot 16}$

Step 1.2.2

Multiply $- 4 \cdot 16 \cdot 240$ .

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Step 1.2.2.1

Multiply $- 4$ by $16$ .

$\frac{128 - v (16384 - 64 \cdot 240)}{2 \cdot 16}$

Step 1.2.2.2

Multiply $- 64$ by $240$ .

$\frac{128 - v (16384 - 15360)}{2 \cdot 16}$

Step 1.3

Subtract $15360$ from $16384$ .

$\frac{128 - v \cdot 1024}{2 \cdot 16}$

Step 1.4

Multiply $1024$ by $- 1$ .

$\frac{128 - 1024 v}{2 \cdot 16}$

Step 1.5

Factor $128$ out of $128 - 1024 v$ .

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Step 1.5.1

Factor $128$ out of $128$ .

$\frac{128 (1) - 1024 v}{2 \cdot 16}$

Step 1.5.2

Factor $128$ out of $- 1024 v$ .

$\frac{128 (1) + 128 (- 8 v)}{2 \cdot 16}$

Step 1.5.3

Factor $128$ out of $128 (1) + 128 (- 8 v)$ .

$\frac{128 (1 - 8 v)}{2 \cdot 16}$

Step 2

Simplify terms.

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Step 2.1

Multiply $2$ by $16$ .

$\frac{128 (1 - 8 v)}{32}$

Step 2.2

Cancel the common factor of $128$ and $32$ .

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Step 2.2.1

Factor $32$ out of $128 (1 - 8 v)$ .

$\frac{32 (4 (1 - 8 v))}{32}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $32$ out of $32$ .

$\frac{32 (4 (1 - 8 v))}{32 (1)}$

Step 2.2.2.2

Cancel the common factor.

$\frac{32 (4 (1 - 8 v))}{32 \cdot 1}$

Step 2.2.2.3

Rewrite the expression.

$\frac{4 (1 - 8 v)}{1}$

Step 2.2.2.4

Divide $4 (1 - 8 v)$ by $1$ .

$4 (1 - 8 v)$

Step 2.3

Apply the distributive property.

$4 \cdot 1 + 4 (- 8 v)$

Step 2.4

Multiply.

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Step 2.4.1

Multiply $4$ by $1$ .

$4 + 4 (- 8 v)$

Step 2.4.2

Multiply $- 8$ by $4$ .

$4 - 32 v$