What are the solutions to the equation t^5(3t+6)=4(80-2t) ?

The solutions to the equation t^5(3t+6)=4(80-2t) are t\approx 1.91750…,t\approx-2.73913…

Find the zeros of t^5(3t+6)=4(80-2t)

The zeros of t^5(3t+6)=4(80-2t) are t\approx 1.91750…,t\approx-2.73913…

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t^{5} (3 t + 6) = 4 (80 - 2 t)

t \approx 1.91750 \dots, t \approx - 2.73913 \dots

Solution steps

t^{5} (3 t + 6) = 4 (80 - 2 t)

Expand

t^{5} (3 t + 6) : 3 t^{6} + 6 t^{5}

Expand

4 (80 - 2 t) : 320 - 8 t

3 t^{6} + 6 t^{5} = 320 - 8 t

Move

8 t

to the left side

3 t^{6} + 6 t^{5} + 8 t = 320

Move

320

to the left side

3 t^{6} + 6 t^{5} + 8 t - 320 = 0

Find one solution for

3 t^{6} + 6 t^{5} + 8 t - 320 = 0

using Newton-Raphson:

t \approx 1.91750 \dots

Apply long division:

\frac{3 t ^{6} + 6 t ^{5} + 8 t - 320}{t - 1.91750 \dots} = 3 t^{5} + 11.75251 \dots t^{4} + 22.53553 \dots t^{3} + 43.21203 \dots t^{2} + 82.85936 \dots t + 166.88338 \dots

3 t^{5} + 11.75251 \dots t^{4} + 22.53553 \dots t^{3} + 43.21203 \dots t^{2} + 82.85936 \dots t + 166.88338 \dots \approx 0

Find one solution for

3 t^{5} + 11.75251 \dots t^{4} + 22.53553 \dots t^{3} + 43.21203 \dots t^{2} + 82.85936 \dots t + 166.88338 \dots = 0

using Newton-Raphson:

t \approx - 2.73913 \dots

Apply long division:

\frac{3 t ^{5} + 11.75251 \dots t ^{4} + 22.53553 \dots t ^{3} + 43.21203 \dots t ^{2} + 82.85936 \dots t + 166.88338 \dots}{t + 2.73913 \dots} = 3 t^{4} + 3.53510 \dots t^{3} + 12.85238 \dots t^{2} + 8.00757 \dots t + 60.92552 \dots

3 t^{4} + 3.53510 \dots t^{3} + 12.85238 \dots t^{2} + 8.00757 \dots t + 60.92552 \dots \approx 0

Find one solution for

3 t^{4} + 3.53510 \dots t^{3} + 12.85238 \dots t^{2} + 8.00757 \dots t + 60.92552 \dots = 0

using Newton-Raphson:

No Solution for

t \in R

The solutions are

t \approx 1.91750 \dots, t \approx - 2.73913 \dots

2 x^{2} (x - 3) = 0

5 - x^{3} = 0

2 b^{4} - 32 = 0

x^{2} = 196 x^{4}

114 x^{4} - 2 4^{2} + 1 = 0

What are the solutions to the equation t^5(3t+6)=4(80-2t) ?
The solutions to the equation t^5(3t+6)=4(80-2t) are t\approx 1.91750…,t\approx-2.73913…
Find the zeros of t^5(3t+6)=4(80-2t)
The zeros of t^5(3t+6)=4(80-2t) are t\approx 1.91750…,t\approx-2.73913…