Finite Math Examples

$- σ^{3} + 9.96 σ^{2} + 384.47 σ - 2095.37 = 0$

Step 1

Factor $0.01$ out of $- σ^{3} + 9.96 σ^{2} + 384.47 σ - 2095.37$ .

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Step 1.1

Factor $0.01$ out of $- σ^{3}$ .

$0.01 (- 100 σ^{3}) + 9.96 σ^{2} + 384.47 σ - 2095.37 = 0$

Step 1.2

Factor $0.01$ out of $9.96 σ^{2}$ .

$0.01 (- 100 σ^{3}) + 0.01 (996 σ^{2}) + 384.47 σ - 2095.37 = 0$

Step 1.3

Factor $0.01$ out of $384.47 σ$ .

$0.01 (- 100 σ^{3}) + 0.01 (996 σ^{2}) + 0.01 (38447 σ) - 2095.37 = 0$

Step 1.4

Factor $0.01$ out of $- 2095.37$ .

$0.01 (- 100 σ^{3}) + 0.01 (996 σ^{2}) + 0.01 (38447 σ) + 0.01 (- 209537) = 0$

Step 1.5

Factor $0.01$ out of $0.01 (- 100 σ^{3}) + 0.01 (996 σ^{2})$ .

$0.01 (- 100 σ^{3} + 996 σ^{2}) + 0.01 (38447 σ) + 0.01 (- 209537) = 0$

Step 1.6

Factor $0.01$ out of $0.01 (- 100 σ^{3} + 996 σ^{2}) + 0.01 (38447 σ)$ .

$0.01 (- 100 σ^{3} + 996 σ^{2} + 38447 σ) + 0.01 (- 209537) = 0$

Step 1.7

Factor $0.01$ out of $0.01 (- 100 σ^{3} + 996 σ^{2} + 38447 σ) + 0.01 (- 209537)$ .

$0.01 (- 100 σ^{3} + 996 σ^{2} + 38447 σ - 209537) = 0$

Step 2

Simplify $0.01 (- 100 σ^{3} + 996 σ^{2} + 38447 σ - 209537)$ .

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Step 2.1

Apply the distributive property.

$0.01 (- 100 σ^{3}) + 0.01 (996 σ^{2}) + 0.01 (38447 σ) + 0.01 \cdot - 209537 = 0$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 100$ by $0.01$ .

$- 1 σ^{3} + 0.01 (996 σ^{2}) + 0.01 (38447 σ) + 0.01 \cdot - 209537 = 0$

Step 2.2.2

Multiply $996$ by $0.01$ .

$- 1 σ^{3} + 9.96 σ^{2} + 0.01 (38447 σ) + 0.01 \cdot - 209537 = 0$

Step 2.2.3

Multiply $38447$ by $0.01$ .

$- 1 σ^{3} + 9.96 σ^{2} + 384.47 σ + 0.01 \cdot - 209537 = 0$

Step 2.2.4

Multiply $0.01$ by $- 209537$ .

$- 1 σ^{3} + 9.96 σ^{2} + 384.47 σ - 2095.37 = 0$

Step 2.3

Rewrite $- 1 σ^{3}$ as $- σ^{3}$ .

$- σ^{3} + 9.96 σ^{2} + 384.47 σ - 2095.37 = 0$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$σ \approx - 17.95418601, 5.12001447, 22.79417154$

Step 4