What are the solutions to the equation x=2+(3x^5-2)-(3+3x^2) ?

The solutions to the equation x=2+(3x^5-2)-(3+3x^2) are x\approx 1.24213…

Find the zeros of x=2+(3x^5-2)-(3+3x^2)

The zeros of x=2+(3x^5-2)-(3+3x^2) are x\approx 1.24213…

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x = 2 + (3 x^{5} - 2) - (3 + 3 x^{2})

x \approx 1.24213 \dots

Solution steps

x = 2 + (3 x^{5} - 2) - (3 + 3 x^{2})

Expand

2 + (3 x^{5} - 2) - (3 + 3 x^{2}) : 3 x^{5} - 3 x^{2} - 3

x = 3 x^{5} - 3 x^{2} - 3

Switch sides

3 x^{5} - 3 x^{2} - 3 = x

Move

x

to the left side

3 x^{5} - 3 x^{2} - 3 - x = 0

Write in the standard form

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

3 x^{5} - 3 x^{2} - x - 3 = 0

Find one solution for

3 x^{5} - 3 x^{2} - x - 3 = 0

using Newton-Raphson:

x \approx 1.24213 \dots

Apply long division:

\frac{3 x ^{5} - 3 x ^{2} - x - 3}{x - 1.24213 \dots} = 3 x^{4} + 3.72640 \dots x^{3} + 4.62869 \dots x^{2} + 2.74945 \dots x + 2.41519 \dots

3 x^{4} + 3.72640 \dots x^{3} + 4.62869 \dots x^{2} + 2.74945 \dots x + 2.41519 \dots \approx 0

Find one solution for

3 x^{4} + 3.72640 \dots x^{3} + 4.62869 \dots x^{2} + 2.74945 \dots x + 2.41519 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.24213 \dots

x^{3} - 7 x^{2} + 12 x = 0

(3 x - 2) (x^{2} - 5) = 0

x^{3} - 4 x^{2} + 9 x - 10 = 0

z^{6} - 2 i = 0

4 x^{3} - 7 x + 3 = 0

What are the solutions to the equation x=2+(3x^5-2)-(3+3x^2) ?
The solutions to the equation x=2+(3x^5-2)-(3+3x^2) are x\approx 1.24213…
Find the zeros of x=2+(3x^5-2)-(3+3x^2)
The zeros of x=2+(3x^5-2)-(3+3x^2) are x\approx 1.24213…