What are the solutions to the equation (x-3)^3+x(1-x)=3 ?

The solutions to the equation (x-3)^3+x(1-x)=3 are x\approx 6.32130…

Find the zeros of (x-3)^3+x(1-x)=3

The zeros of (x-3)^3+x(1-x)=3 are x\approx 6.32130…

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(x - 3)^{3} + x (1 - x) = 3

x \approx 6.32130 \dots

Solution steps

(x - 3)^{3} + x (1 - x) = 3

Expand

(x - 3)^{3} + x (1 - x) : x^{3} - 10 x^{2} + 28 x - 27

x^{3} - 10 x^{2} + 28 x - 27 = 3

Move

3

to the left side

x^{3} - 10 x^{2} + 28 x - 30 = 0

Find one solution for

x^{3} - 10 x^{2} + 28 x - 30 = 0

using Newton-Raphson:

x \approx 6.32130 \dots

Apply long division:

\frac{x ^{3} - 10 x ^{2} + 28 x - 30}{x - 6.32130 \dots} = x^{2} - 3.67869 \dots x + 4.74585 \dots

x^{2} - 3.67869 \dots x + 4.74585 \dots \approx 0

Find one solution for

x^{2} - 3.67869 \dots x + 4.74585 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 6.32130 \dots

y^{(5)} - y^{(4)} = 0

x^{3} + \frac{1}{2} x^{2} + x - 3 = 0

x x^{3} + 144 x^{2} = 4096

(x^{2} + 3) (x - 8) = 0

2 x^{3} + 3 x^{2} + 23 x - 12 = 0

What are the solutions to the equation (x-3)^3+x(1-x)=3 ?
The solutions to the equation (x-3)^3+x(1-x)=3 are x\approx 6.32130…
Find the zeros of (x-3)^3+x(1-x)=3
The zeros of (x-3)^3+x(1-x)=3 are x\approx 6.32130…