What are the solutions to the equation 8x^1+x^2+2x^3+x^4=8 ?

The solutions to the equation 8x^1+x^2+2x^3+x^4=8 are x\approx 0.76882…,x\approx-2.91844…

Find the zeros of 8x^1+x^2+2x^3+x^4=8

The zeros of 8x^1+x^2+2x^3+x^4=8 are x\approx 0.76882…,x\approx-2.91844…

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8 x^{1} + x^{2} + 2 x^{3} + x^{4} = 8

x \approx 0.76882 \dots, x \approx - 2.91844 \dots

Solution steps

8 x^{1} + x^{2} + 2 x^{3} + x^{4} = 8

Refine

8 x + x^{2} + 2 x^{3} + x^{4} = 8

Move

8

to the left side

8 x + x^{2} + 2 x^{3} + x^{4} - 8 = 0

Write in the standard form

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

x^{4} + 2 x^{3} + x^{2} + 8 x - 8 = 0

Find one solution for

x^{4} + 2 x^{3} + x^{2} + 8 x - 8 = 0

using Newton-Raphson:

x \approx 0.76882 \dots

Apply long division:

\frac{x ^{4} + 2 x ^{3} + x ^{2} + 8 x - 8}{x - 0.76882 \dots} = x^{3} + 2.76882 \dots x^{2} + 3.12874 \dots x + 10.40546 \dots

x^{3} + 2.76882 \dots x^{2} + 3.12874 \dots x + 10.40546 \dots \approx 0

Find one solution for

x^{3} + 2.76882 \dots x^{2} + 3.12874 \dots x + 10.40546 \dots = 0

using Newton-Raphson:

x \approx - 2.91844 \dots

Apply long division:

\frac{x ^{3} + 2.76882 \dots x ^{2} + 3.12874 \dots x + 10.40546 \dots}{x + 2.91844 \dots} = x^{2} - 0.14962 \dots x + 3.56541 \dots

x^{2} - 0.14962 \dots x + 3.56541 \dots \approx 0

Find one solution for

x^{2} - 0.14962 \dots x + 3.56541 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.76882 \dots, x \approx - 2.91844 \dots

x, y^{2} + 1 = x^{3}

x^{4} - 4 x^{3} + 8 x^{2} - 8 x + 4 = 0

x^{4} - x^{2} - 1 = 0

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

(x) = (x^{3} + 8) \cdot (3 x - 15)

What are the solutions to the equation 8x^1+x^2+2x^3+x^4=8 ?
The solutions to the equation 8x^1+x^2+2x^3+x^4=8 are x\approx 0.76882…,x\approx-2.91844…
Find the zeros of 8x^1+x^2+2x^3+x^4=8
The zeros of 8x^1+x^2+2x^3+x^4=8 are x\approx 0.76882…,x\approx-2.91844…