What are the solutions to the equation 7\times x-9=4\times x^{27} ?

The solutions to the equation 7\times x-9=4\times x^{27} are x\approx-1.05358…

Find the zeros of 7\times x-9=4\times x^{27}

The zeros of 7\times x-9=4\times x^{27} are x\approx-1.05358…

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7 \cdot x - 9 = 4 \cdot x^{27}

x \approx - 1.05358 \dots

Solution steps

7 x - 9 = 4 x^{27}

Switch sides

4 x^{27} = 7 x - 9

Move

9

to the left side

4 x^{27} + 9 = 7 x

Move

7 x

to the left side

4 x^{27} + 9 - 7 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 x^{27} - 7 x + 9 = 0

Find one solution for

4 x^{27} - 7 x + 9 = 0

using Newton-Raphson:

x \approx - 1.05358 \dots

Apply long division:

\frac{4 x ^{27} - 7 x + 9}{x + 1.05358 \dots} = 4 x^{26} - 4.21435 \dots x^{25} + 4.44020 \dots x^{24} - 4.67814 \dots x^{23} + 4.92884 \dots x^{22} - 5.19297 \dots x^{21} + 5.47126 \dots x^{20} - 5.76446 \dots x^{19} + 6.07337 \dots x^{18} - 6.39884 \dots x^{17} + 6.74175 \dots x^{16} - 7.10303 \dots x^{15} + 7.48368 \dots x^{14} - 7.88472 \dots x^{13} + 8.30726 \dots x^{12} - 8.75244 \dots x^{11} + 9.22147 \dots x^{10} - 9.71564 \dots x^{9} + 10.23630 \dots x^{8} - 10.78485 \dots x^{7} + 11.36280 \dots x^{6} - 11.97172 \dots x^{5} + 12.61328 \dots x^{4} - 13.28921 \dots x^{3} + 14.00137 \dots x^{2} - 14.75169 \dots x + 8.54222 \dots

4 x^{26} - 4.21435 \dots x^{25} + 4.44020 \dots x^{24} - 4.67814 \dots x^{23} + 4.92884 \dots x^{22} - 5.19297 \dots x^{21} + 5.47126 \dots x^{20} - 5.76446 \dots x^{19} + 6.07337 \dots x^{18} - 6.39884 \dots x^{17} + 6.74175 \dots x^{16} - 7.10303 \dots x^{15} + 7.48368 \dots x^{14} - 7.88472 \dots x^{13} + 8.30726 \dots x^{12} - 8.75244 \dots x^{11} + 9.22147 \dots x^{10} - 9.71564 \dots x^{9} + 10.23630 \dots x^{8} - 10.78485 \dots x^{7} + 11.36280 \dots x^{6} - 11.97172 \dots x^{5} + 12.61328 \dots x^{4} - 13.28921 \dots x^{3} + 14.00137 \dots x^{2} - 14.75169 \dots x + 8.54222 \dots \approx 0

Find one solution for

4 x^{26} - 4.21435 \dots x^{25} + 4.44020 \dots x^{24} - 4.67814 \dots x^{23} + 4.92884 \dots x^{22} - 5.19297 \dots x^{21} + 5.47126 \dots x^{20} - 5.76446 \dots x^{19} + 6.07337 \dots x^{18} - 6.39884 \dots x^{17} + 6.74175 \dots x^{16} - 7.10303 \dots x^{15} + 7.48368 \dots x^{14} - 7.88472 \dots x^{13} + 8.30726 \dots x^{12} - 8.75244 \dots x^{11} + 9.22147 \dots x^{10} - 9.71564 \dots x^{9} + 10.23630 \dots x^{8} - 10.78485 \dots x^{7} + 11.36280 \dots x^{6} - 11.97172 \dots x^{5} + 12.61328 \dots x^{4} - 13.28921 \dots x^{3} + 14.00137 \dots x^{2} - 14.75169 \dots x + 8.54222 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.05358 \dots

t^{4} - 3 t^{3} - 40 t^{2} = 0

y, 2 x^{3} - 3 y^{2} = 8

x^{8} - 2 x^{4} + 4 = 0

67500 x^{3} + 48780000 x = 0

x^{3} - 3 x^{2} - 13 x + 15 = 0

What are the solutions to the equation 7\times x-9=4\times x^{27} ?
The solutions to the equation 7\times x-9=4\times x^{27} are x\approx-1.05358…
Find the zeros of 7\times x-9=4\times x^{27}
The zeros of 7\times x-9=4\times x^{27} are x\approx-1.05358…