What are the solutions to the equation (10x+1)+(5x^{29})=180 ?

The solutions to the equation (10x+1)+(5x^{29})=180 are x\approx 1.12877…

Find the zeros of (10x+1)+(5x^{29})=180

The zeros of (10x+1)+(5x^{29})=180 are x\approx 1.12877…

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(10 x + 1) + (5 x^{29}) = 180

x \approx 1.12877 \dots

Solution steps

(10 x + 1) + (5 x^{29}) = 180

Refine

10 x + 1 + 5 x^{29} = 180

Move

180

to the left side

5 x^{29} + 10 x - 179 = 0

Find one solution for

5 x^{29} + 10 x - 179 = 0

using Newton-Raphson:

x \approx 1.12877 \dots

Apply long division:

\frac{5 x ^{29} + 10 x - 179}{x - 1.12877 \dots} = 5 x^{28} + 5.64386 \dots x^{27} + 6.37064 \dots x^{26} + 7.19101 \dots x^{25} + 8.11702 \dots x^{24} + 9.16228 \dots x^{23} + 10.34213 \dots x^{22} + 11.67392 \dots x^{21} + 13.17721 \dots x^{20} + 14.87409 \dots x^{19} + 16.78947 \dots x^{18} + 18.95151 \dots x^{17} + 21.39196 \dots x^{16} + 24.14667 \dots x^{15} + 27.25612 \dots x^{14} + 30.76598 \dots x^{13} + 34.72781 \dots x^{12} + 39.19983 \dots x^{11} + 44.24772 \dots x^{10} + 49.94564 \dots x^{9} + 56.37731 \dots x^{8} + 63.63720 \dots x^{7} + 71.83197 \dots x^{6} + 81.08201 \dots x^{5} + 91.52320 \dots x^{4} + 103.30895 \dots x^{3} + 116.61238 \dots x^{2} + 131.62894 \dots x + 158.57923 \dots

5 x^{28} + 5.64386 \dots x^{27} + 6.37064 \dots x^{26} + 7.19101 \dots x^{25} + 8.11702 \dots x^{24} + 9.16228 \dots x^{23} + 10.34213 \dots x^{22} + 11.67392 \dots x^{21} + 13.17721 \dots x^{20} + 14.87409 \dots x^{19} + 16.78947 \dots x^{18} + 18.95151 \dots x^{17} + 21.39196 \dots x^{16} + 24.14667 \dots x^{15} + 27.25612 \dots x^{14} + 30.76598 \dots x^{13} + 34.72781 \dots x^{12} + 39.19983 \dots x^{11} + 44.24772 \dots x^{10} + 49.94564 \dots x^{9} + 56.37731 \dots x^{8} + 63.63720 \dots x^{7} + 71.83197 \dots x^{6} + 81.08201 \dots x^{5} + 91.52320 \dots x^{4} + 103.30895 \dots x^{3} + 116.61238 \dots x^{2} + 131.62894 \dots x + 158.57923 \dots \approx 0

Find one solution for

5 x^{28} + 5.64386 \dots x^{27} + 6.37064 \dots x^{26} + 7.19101 \dots x^{25} + 8.11702 \dots x^{24} + 9.16228 \dots x^{23} + 10.34213 \dots x^{22} + 11.67392 \dots x^{21} + 13.17721 \dots x^{20} + 14.87409 \dots x^{19} + 16.78947 \dots x^{18} + 18.95151 \dots x^{17} + 21.39196 \dots x^{16} + 24.14667 \dots x^{15} + 27.25612 \dots x^{14} + 30.76598 \dots x^{13} + 34.72781 \dots x^{12} + 39.19983 \dots x^{11} + 44.24772 \dots x^{10} + 49.94564 \dots x^{9} + 56.37731 \dots x^{8} + 63.63720 \dots x^{7} + 71.83197 \dots x^{6} + 81.08201 \dots x^{5} + 91.52320 \dots x^{4} + 103.30895 \dots x^{3} + 116.61238 \dots x^{2} + 131.62894 \dots x + 158.57923 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.12877 \dots

240 x - 60 x^{3} = 0

2 x^{3} - 3 x^{2} - 14 x + 21 = 0

7 x^{2} + 15 x = 2 x^{3}

x^{4} - x^{3} - 3 x^{2} + 5 x - 2 = 0

x^{3} - 34 x + 12 = 0

What are the solutions to the equation (10x+1)+(5x^{29})=180 ?
The solutions to the equation (10x+1)+(5x^{29})=180 are x\approx 1.12877…
Find the zeros of (10x+1)+(5x^{29})=180
The zeros of (10x+1)+(5x^{29})=180 are x\approx 1.12877…