Finite Math Examples

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

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

Step 1

Factor

0.01

$0.01$ out of

- σ^{3} + 9.96 σ^{2} + 384.47 σ - 2095.37

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

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Step 1.1

Factor

0.01

$0.01$ out of

- σ^{3}

$- σ^{3}$ .

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

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

Step 1.2

Factor

0.01

$0.01$ out of

9.96 σ^{2}

$9.96 σ^{2}$ .

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

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

Step 1.3

Factor

0.01

$0.01$ out of

384.47 σ

$384.47 σ$ .

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

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

Step 1.4

Factor

0.01

$0.01$ out of

- 2095.37

$- 2095.37$ .

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

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

Step 1.5

Factor

0.01

$0.01$ out of

0.01 (- 100 σ^{3}) + 0.01 (996 σ^{2})

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

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

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

Step 1.6

Factor

0.01

$0.01$ out of

0.01 (- 100 σ^{3} + 996 σ^{2}) + 0.01 (38447 σ)

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

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

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

Step 1.7

Factor

0.01

$0.01$ out of

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

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

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

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

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

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

Step 2

Simplify

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

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

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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

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply

- 100

$- 100$ by

0.01

$0.01$ .

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

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

Step 2.2.2

Multiply

996

$996$ by

0.01

$0.01$ .

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

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

Step 2.2.3

Multiply

38447

$38447$ by

0.01

$0.01$ .

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

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

Step 2.2.4

Multiply

0.01

$0.01$ by

- 209537

$- 209537$ .

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

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

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

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

Step 2.3

Rewrite

- 1 σ^{3}

$- 1 σ^{3}$ as

- σ^{3}

$- σ^{3}$ .

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

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

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

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

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

$σ \approx - 17.95418601, 5.12001447, 22.79417154$

Step 4