What are the solutions to the equation x(x-4)^2-11=5 ?

The solutions to the equation x(x-4)^2-11=5 are x\approx 5.67857…

Find the zeros of x(x-4)^2-11=5

The zeros of x(x-4)^2-11=5 are x\approx 5.67857…

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x (x - 4)^{2} - 11 = 5

x \approx 5.67857 \dots

Solution steps

x (x - 4)^{2} - 11 = 5

Expand

x (x - 4)^{2} - 11 : x^{3} - 8 x^{2} + 16 x - 11

x^{3} - 8 x^{2} + 16 x - 11 = 5

Move

5

to the left side

x^{3} - 8 x^{2} + 16 x - 16 = 0

Find one solution for

x^{3} - 8 x^{2} + 16 x - 16 = 0

using Newton-Raphson:

x \approx 5.67857 \dots

Apply long division:

\frac{x ^{3} - 8 x ^{2} + 16 x - 16}{x - 5.67857 \dots} = x^{2} - 2.32142 \dots x + 2.81760 \dots

x^{2} - 2.32142 \dots x + 2.81760 \dots \approx 0

Find one solution for

x^{2} - 2.32142 \dots x + 2.81760 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 5.67857 \dots

x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x = 0

x^{3} - 6 x^{2} + 11 x + 6 = 0

x^{3} = 27 x^{10}

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

(x + 1)^{4} = (2 x)^{4}

What are the solutions to the equation x(x-4)^2-11=5 ?
The solutions to the equation x(x-4)^2-11=5 are x\approx 5.67857…
Find the zeros of x(x-4)^2-11=5
The zeros of x(x-4)^2-11=5 are x\approx 5.67857…