What are the solutions to the equation x^5+4x^4+4=-4 ?

The solutions to the equation x^5+4x^4+4=-4 are x\approx-4.03032…

Find the zeros of x^5+4x^4+4=-4

The zeros of x^5+4x^4+4=-4 are x\approx-4.03032…

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x^{5} + 4 x^{4} + 4 = - 4

x \approx - 4.03032 \dots

Solution steps

x^{5} + 4 x^{4} + 4 = - 4

Move

4

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx - 4.03032 \dots

Apply long division:

\frac{x ^{5} + 4 x ^{4} + 8}{x + 4.03032 \dots} = x^{4} - 0.03032 \dots x^{3} + 0.12220 \dots x^{2} - 0.49250 \dots x + 1.98495 \dots

x^{4} - 0.03032 \dots x^{3} + 0.12220 \dots x^{2} - 0.49250 \dots x + 1.98495 \dots \approx 0

Find one solution for

x^{4} - 0.03032 \dots x^{3} + 0.12220 \dots x^{2} - 0.49250 \dots x + 1.98495 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 4.03032 \dots

- 83 = b^{4} b^{4}

y, y^{4} = x

h^{4} = 3

x^{3} = 3 x - 2

x x^{2} - 7 x = 180

What are the solutions to the equation x^5+4x^4+4=-4 ?
The solutions to the equation x^5+4x^4+4=-4 are x\approx-4.03032…
Find the zeros of x^5+4x^4+4=-4
The zeros of x^5+4x^4+4=-4 are x\approx-4.03032…