What are the solutions to the equation t=-t^3+10t^2-29t+29 ?

The solutions to the equation t=-t^3+10t^2-29t+29 are t\approx 5.51154…

Find the zeros of t=-t^3+10t^2-29t+29

The zeros of t=-t^3+10t^2-29t+29 are t\approx 5.51154…

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t = - t^{3} + 10 t^{2} - 29 t + 29

t \approx 5.51154 \dots

Solution steps

t = - t^{3} + 10 t^{2} - 29 t + 29

Switch sides

- t^{3} + 10 t^{2} - 29 t + 29 = t

Move

t

to the left side

- t^{3} + 10 t^{2} - 30 t + 29 = 0

Find one solution for

- t^{3} + 10 t^{2} - 30 t + 29 = 0

using Newton-Raphson:

t \approx 5.51154 \dots

Apply long division:

\frac{- t ^{3} + 10 t ^{2} - 30 t + 29}{t - 5.51154 \dots} = - t^{2} + 4.48845 \dots t - 5.26168 \dots

- t^{2} + 4.48845 \dots t - 5.26168 \dots \approx 0

Find one solution for

- t^{2} + 4.48845 \dots t - 5.26168 \dots = 0

using Newton-Raphson:

No Solution for

t \in R

The solution is

t \approx 5.51154 \dots

2 x^{3} + 3 x^{2} - 12 x + 6 = 0

x^{3} + 3 x^{2} + 2 x + 1 = 0

x^{3} - 12 x^{2} + 48 x - 63 = 0

0 = x^{3} - 7 x + 6

s, s (s + 2) (s + 10) = 0

What are the solutions to the equation t=-t^3+10t^2-29t+29 ?
The solutions to the equation t=-t^3+10t^2-29t+29 are t\approx 5.51154…
Find the zeros of t=-t^3+10t^2-29t+29
The zeros of t=-t^3+10t^2-29t+29 are t\approx 5.51154…