What are the solutions to the equation f=f^8-23710 ?

The solutions to the equation f=f^8-23710 are f\approx-3.52255…,f\approx 3.52269…

Find the zeros of f=f^8-23710

The zeros of f=f^8-23710 are f\approx-3.52255…,f\approx 3.52269…

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f = f^{8} - 23710

f \approx - 3.52255 \dots, f \approx 3.52269 \dots

Solution steps

f = f^{8} - 23710

Switch sides

f^{8} - 23710 = f

Move

f

to the left side

f^{8} - 23710 - f = 0

Write in the standard form

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

f^{8} - f - 23710 = 0

Find one solution for

f^{8} - f - 23710 = 0

using Newton-Raphson:

f \approx - 3.52255 \dots

Apply long division:

\frac{f ^{8} - f - 23710}{f + 3.52255 \dots} = f^{7} - 3.52255 \dots f^{6} + 12.40842 \dots f^{5} - 43.70942 \dots f^{4} + 153.96907 \dots f^{3} - 542.36529 \dots f^{2} + 1910.51420 \dots f - 6730.90057 \dots

f^{7} - 3.52255 \dots f^{6} + 12.40842 \dots f^{5} - 43.70942 \dots f^{4} + 153.96907 \dots f^{3} - 542.36529 \dots f^{2} + 1910.51420 \dots f - 6730.90057 \dots \approx 0

Find one solution for

f^{7} - 3.52255 \dots f^{6} + 12.40842 \dots f^{5} - 43.70942 \dots f^{4} + 153.96907 \dots f^{3} - 542.36529 \dots f^{2} + 1910.51420 \dots f - 6730.90057 \dots = 0

using Newton-Raphson:

f \approx 3.52269 \dots

Apply long division:

\frac{f ^{7} - 3.52255 \dots f ^{6} + 12.40842 \dots f ^{5} - 43.70942 \dots f ^{4} + 153.96907 \dots f ^{3} - 542.36529 \dots f ^{2} + 1910.51420 \dots f - 6730.90057 \dots}{f - 3.52269 \dots} = f^{6} + 0.00013 \dots f^{5} + 12.40888 \dots f^{4} + 0.00324 \dots f^{3} + 153.98051 \dots f^{2} + 0.06044 \dots f + 1910.72711 \dots

f^{6} + 0.00013 \dots f^{5} + 12.40888 \dots f^{4} + 0.00324 \dots f^{3} + 153.98051 \dots f^{2} + 0.06044 \dots f + 1910.72711 \dots \approx 0

Find one solution for

f^{6} + 0.00013 \dots f^{5} + 12.40888 \dots f^{4} + 0.00324 \dots f^{3} + 153.98051 \dots f^{2} + 0.06044 \dots f + 1910.72711 \dots = 0

using Newton-Raphson:

No Solution for

f \in R

The solutions are

f \approx - 3.52255 \dots, f \approx 3.52269 \dots

y = (5 x + 2) (x^{2} + 5)

f (x) = \frac{x ^{4} - x ^{3}}{3}

f (x) = x - 4 x - 5

f (x) = \frac{1}{( x + e ^{2 x} )}

f (x) = x^{2} + 16 x + 39

What are the solutions to the equation f=f^8-23710 ?
The solutions to the equation f=f^8-23710 are f\approx-3.52255…,f\approx 3.52269…
Find the zeros of f=f^8-23710
The zeros of f=f^8-23710 are f\approx-3.52255…,f\approx 3.52269…