What are the solutions to the equation 2x-53=2+x^{15} ?

The solutions to the equation 2x-53=2+x^{15} are x\approx-1.31030…

Find the zeros of 2x-53=2+x^{15}

The zeros of 2x-53=2+x^{15} are x\approx-1.31030…

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2 x - 53 = 2 + x^{15}

x \approx - 1.31030 \dots

Solution steps

2 x - 53 = 2 + x^{15}

Switch sides

2 + x^{15} = 2 x - 53

Move

53

to the left side

x^{15} + 55 = 2 x

Move

2 x

to the left side

x^{15} + 55 - 2 x = 0

Write in the standard form

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

x^{15} - 2 x + 55 = 0

Find one solution for

x^{15} - 2 x + 55 = 0

using Newton-Raphson:

x \approx - 1.31030 \dots

Apply long division:

\frac{x ^{15} - 2 x + 55}{x + 1.31030 \dots} = x^{14} - 1.31030 \dots x^{13} + 1.71689 \dots x^{12} - 2.24965 \dots x^{11} + 2.94772 \dots x^{10} - 3.86241 \dots x^{9} + 5.06093 \dots x^{8} - 6.63136 \dots x^{7} + 8.68910 \dots x^{6} - 11.38535 \dots x^{5} + 14.91827 \dots x^{4} - 19.54746 \dots x^{3} + 25.61310 \dots x^{2} - 33.56094 \dots x + 41.97501 \dots

x^{14} - 1.31030 \dots x^{13} + 1.71689 \dots x^{12} - 2.24965 \dots x^{11} + 2.94772 \dots x^{10} - 3.86241 \dots x^{9} + 5.06093 \dots x^{8} - 6.63136 \dots x^{7} + 8.68910 \dots x^{6} - 11.38535 \dots x^{5} + 14.91827 \dots x^{4} - 19.54746 \dots x^{3} + 25.61310 \dots x^{2} - 33.56094 \dots x + 41.97501 \dots \approx 0

Find one solution for

x^{14} - 1.31030 \dots x^{13} + 1.71689 \dots x^{12} - 2.24965 \dots x^{11} + 2.94772 \dots x^{10} - 3.86241 \dots x^{9} + 5.06093 \dots x^{8} - 6.63136 \dots x^{7} + 8.68910 \dots x^{6} - 11.38535 \dots x^{5} + 14.91827 \dots x^{4} - 19.54746 \dots x^{3} + 25.61310 \dots x^{2} - 33.56094 \dots x + 41.97501 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.31030 \dots

5 g^{2} + g^{3} = - 4 g

x^{4} + 35 x^{2} - 36 = 0

4 x^{3} = 256 x

2 x^{4} + 8 x^{2} + 5 = 0

x, x^{3} = 27

What are the solutions to the equation 2x-53=2+x^{15} ?
The solutions to the equation 2x-53=2+x^{15} are x\approx-1.31030…
Find the zeros of 2x-53=2+x^{15}
The zeros of 2x-53=2+x^{15} are x\approx-1.31030…