What are the solutions to the equation t^{16}-2t=t+9+4t ?

The solutions to the equation t^{16}-2t=t+9+4t are t\approx-1.03561…,t\approx 1.19531…

Find the zeros of t^{16}-2t=t+9+4t

The zeros of t^{16}-2t=t+9+4t are t\approx-1.03561…,t\approx 1.19531…

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t^{16} - 2 t = t + 9 + 4 t

t \approx - 1.03561 \dots, t \approx 1.19531 \dots

Solution steps

t^{16} - 2 t = t + 9 + 4 t

Refine

t^{16} - 2 t = 5 t + 9

Move

9

to the left side

t^{16} - 2 t - 9 = 5 t

Move

5 t

to the left side

t^{16} - 7 t - 9 = 0

Find one solution for

t^{16} - 7 t - 9 = 0

using Newton-Raphson:

t \approx - 1.03561 \dots

Apply long division:

\frac{t ^{16} - 7 t - 9}{t + 1.03561 \dots} = t^{15} - 1.03561 \dots t^{14} + 1.07250 \dots t^{13} - 1.11070 \dots t^{12} + 1.15027 \dots t^{11} - 1.19124 \dots t^{10} + 1.23367 \dots t^{9} - 1.27761 \dots t^{8} + 1.32312 \dots t^{7} - 1.37025 \dots t^{6} + 1.41906 \dots t^{5} - 1.46960 \dots t^{4} + 1.52195 \dots t^{3} - 1.57616 \dots t^{2} + 1.63230 \dots t - 8.69045 \dots

t^{15} - 1.03561 \dots t^{14} + 1.07250 \dots t^{13} - 1.11070 \dots t^{12} + 1.15027 \dots t^{11} - 1.19124 \dots t^{10} + 1.23367 \dots t^{9} - 1.27761 \dots t^{8} + 1.32312 \dots t^{7} - 1.37025 \dots t^{6} + 1.41906 \dots t^{5} - 1.46960 \dots t^{4} + 1.52195 \dots t^{3} - 1.57616 \dots t^{2} + 1.63230 \dots t - 8.69045 \dots \approx 0

Find one solution for

t^{15} - 1.03561 \dots t^{14} + 1.07250 \dots t^{13} - 1.11070 \dots t^{12} + 1.15027 \dots t^{11} - 1.19124 \dots t^{10} + 1.23367 \dots t^{9} - 1.27761 \dots t^{8} + 1.32312 \dots t^{7} - 1.37025 \dots t^{6} + 1.41906 \dots t^{5} - 1.46960 \dots t^{4} + 1.52195 \dots t^{3} - 1.57616 \dots t^{2} + 1.63230 \dots t - 8.69045 \dots = 0

using Newton-Raphson:

t \approx 1.19531 \dots

Apply long division:

\frac{t ^{15} - 1.03561 \dots t ^{14} + 1.07250 \dots t ^{13} - 1.11070 \dots t ^{12} + 1.15027 \dots t ^{11} - 1.19124 \dots t ^{10} + 1.23367 \dots t ^{9} - 1.27761 \dots t ^{8} + 1.32312 \dots t ^{7} - 1.37025 \dots t ^{6} + 1.41906 \dots t ^{5} - 1.46960 \dots t ^{4} + 1.52195 \dots t ^{3} - 1.57616 \dots t ^{2} + 1.63230 \dots t - 8.69045 \dots}{t - 1.19531 \dots} = t^{14} + 0.15969 \dots t^{13} + 1.26339 \dots t^{12} + 0.39945 \dots t^{11} + 1.62774 \dots t^{10} + 0.75442 \dots t^{9} + 2.13545 \dots t^{8} + 1.27492 \dots t^{7} + 2.84706 \dots t^{6} + 2.03288 \dots t^{5} + 3.84901 \dots t^{4} + 3.13117 \dots t^{3} + 5.26470 \dots t^{2} + 4.71682 \dots t + 7.27041 \dots

t^{14} + 0.15969 \dots t^{13} + 1.26339 \dots t^{12} + 0.39945 \dots t^{11} + 1.62774 \dots t^{10} + 0.75442 \dots t^{9} + 2.13545 \dots t^{8} + 1.27492 \dots t^{7} + 2.84706 \dots t^{6} + 2.03288 \dots t^{5} + 3.84901 \dots t^{4} + 3.13117 \dots t^{3} + 5.26470 \dots t^{2} + 4.71682 \dots t + 7.27041 \dots \approx 0

Find one solution for

t^{14} + 0.15969 \dots t^{13} + 1.26339 \dots t^{12} + 0.39945 \dots t^{11} + 1.62774 \dots t^{10} + 0.75442 \dots t^{9} + 2.13545 \dots t^{8} + 1.27492 \dots t^{7} + 2.84706 \dots t^{6} + 2.03288 \dots t^{5} + 3.84901 \dots t^{4} + 3.13117 \dots t^{3} + 5.26470 \dots t^{2} + 4.71682 \dots t + 7.27041 \dots = 0

using Newton-Raphson:

No Solution for

t \in R

The solutions are

t \approx - 1.03561 \dots, t \approx 1.19531 \dots

x^{3} - 11 x^{2} + 36 x - 36 = 0

x^{5} + x^{4} + 1 = 0

y^{3} + 1 = 0

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

d^{6} + 1 = 0

What are the solutions to the equation t^{16}-2t=t+9+4t ?
The solutions to the equation t^{16}-2t=t+9+4t are t\approx-1.03561…,t\approx 1.19531…
Find the zeros of t^{16}-2t=t+9+4t
The zeros of t^{16}-2t=t+9+4t are t\approx-1.03561…,t\approx 1.19531…