Linear Algebra Examples

$\frac{- (11) - v ({(- 11)}^{2} - 4 \cdot - 16 \cdot 123)}{2 (- 16)}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $11$ .

$\frac{- 11 - v ({(- 11)}^{2} - 4 \cdot - 16 \cdot 123)}{2 (- 16)}$

Step 1.2

Simplify each term.

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Step 1.2.1

Raise $- 11$ to the power of $2$ .

$\frac{- 11 - v (121 - 4 \cdot - 16 \cdot 123)}{2 (- 16)}$

Step 1.2.2

Multiply $- 4 \cdot - 16 \cdot 123$ .

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Step 1.2.2.1

Multiply $- 4$ by $- 16$ .

$\frac{- 11 - v (121 + 64 \cdot 123)}{2 (- 16)}$

Step 1.2.2.2

Multiply $64$ by $123$ .

$\frac{- 11 - v (121 + 7872)}{2 (- 16)}$

Step 1.3

Add $121$ and $7872$ .

$\frac{- 11 - v \cdot 7993}{2 (- 16)}$

Step 1.4

Multiply $7993$ by $- 1$ .

$\frac{- 11 - 7993 v}{2 (- 16)}$

Step 2

Simplify with factoring out.

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Step 2.1

Multiply $2$ by $- 16$ .

$\frac{- 11 - 7993 v}{- 32}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{- 11 - 7993 v}{32}$

Step 2.3

Rewrite $- 11$ as $- 1 (11)$ .

$- \frac{- 1 (11) - 7993 v}{32}$

Step 2.4

Factor $- 1$ out of $- 7993 v$ .

$- \frac{- 1 (11) - (7993 v)}{32}$

Step 2.5

Factor $- 1$ out of $- 1 (11) - (7993 v)$ .

$- \frac{- 1 (11 + 7993 v)}{32}$

Step 2.6

Simplify the expression.

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Step 2.6.1

Move the negative in front of the fraction.

$- - \frac{11 + 7993 v}{32}$

Step 2.6.2

Multiply $- 1$ by $- 1$ .

$1 \frac{11 + 7993 v}{32}$

Step 2.6.3

Multiply $\frac{11 + 7993 v}{32}$ by $1$ .

$\frac{11 + 7993 v}{32}$