What are the solutions to the equation 5=3-1/10 b^3-101b ?

The solutions to the equation 5=3-1/10 b^3-101b are b\approx-0.01980…

Find the zeros of 5=3-1/10 b^3-101b

The zeros of 5=3-1/10 b^3-101b are b\approx-0.01980…

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5 = 3 - \frac{1}{10} b^{3} - 101 b

b \approx - 0.01980 \dots

Solution steps

5 = 3 - \frac{1}{10} b^{3} - 101 b

Multiply both sides by

10

50 = 30 - b^{3} - 1010 b

Switch sides

30 - b^{3} - 1010 b = 50

Move

50

to the left side

- b^{3} - 1010 b - 20 = 0

Find one solution for

- b^{3} - 1010 b - 20 = 0

using Newton-Raphson:

b \approx - 0.01980 \dots

Apply long division:

\frac{- b ^{3} - 1010 b - 20}{b + 0.01980 \dots} = - b^{2} + 0.01980 \dots b - 1010.00039 \dots

- b^{2} + 0.01980 \dots b - 1010.00039 \dots \approx 0

Find one solution for

- b^{2} + 0.01980 \dots b - 1010.00039 \dots = 0

using Newton-Raphson:

No Solution for

b \in R

The solution is

b \approx - 0.01980 \dots

- 6 x^{3} + 36 x^{2} + 42 x = 0

x^{3} - 4 x + 3 = 2.8

x^{3} x = 18

9 = b^{4} - (- 5)

x^{3} - 3 x^{2} - x - 5 = 0

What are the solutions to the equation 5=3-1/10 b^3-101b ?
The solutions to the equation 5=3-1/10 b^3-101b are b\approx-0.01980…
Find the zeros of 5=3-1/10 b^3-101b
The zeros of 5=3-1/10 b^3-101b are b\approx-0.01980…