What are the solutions to the equation x=x^5+5x^3+3 ?

The solutions to the equation x=x^5+5x^3+3 are x\approx-0.87592…

Find the zeros of x=x^5+5x^3+3

The zeros of x=x^5+5x^3+3 are x\approx-0.87592…

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x = x^{5} + 5 x^{3} + 3

x \approx - 0.87592 \dots

Solution steps

x = x^{5} + 5 x^{3} + 3

Switch sides

x^{5} + 5 x^{3} + 3 = x

Move

x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.87592 \dots

Apply long division:

\frac{x ^{5} + 5 x ^{3} - x + 3}{x + 0.87592 \dots} = x^{4} - 0.87592 \dots x^{3} + 5.76725 \dots x^{2} - 5.05170 \dots x + 3.42493 \dots

x^{4} - 0.87592 \dots x^{3} + 5.76725 \dots x^{2} - 5.05170 \dots x + 3.42493 \dots \approx 0

Find one solution for

x^{4} - 0.87592 \dots x^{3} + 5.76725 \dots x^{2} - 5.05170 \dots x + 3.42493 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.87592 \dots

9 a^{3} - 81 a = - 2 a^{2} + 18

x, 175 = 5 x^{3}

3 + 9 x^{8} - 6^{2} = A

m^{3} - 4 m^{2} + 4 m = 0

0.024 = (1 + \frac{x}{12})^{12} - 1

What are the solutions to the equation x=x^5+5x^3+3 ?
The solutions to the equation x=x^5+5x^3+3 are x\approx-0.87592…
Find the zeros of x=x^5+5x^3+3
The zeros of x=x^5+5x^3+3 are x\approx-0.87592…