What are the solutions to the equation x+1=x^3-2x-5 ?

The solutions to the equation x+1=x^3-2x-5 are x\approx 2.35530…

Find the zeros of x+1=x^3-2x-5

The zeros of x+1=x^3-2x-5 are x\approx 2.35530…

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x + 1 = x^{3} - 2 x - 5

x \approx 2.35530 \dots

Solution steps

x + 1 = x^{3} - 2 x - 5

Switch sides

x^{3} - 2 x - 5 = x + 1

Move

1

to the left side

x^{3} - 2 x - 6 = x

Move

x

to the left side

x^{3} - 3 x - 6 = 0

Find one solution for

x^{3} - 3 x - 6 = 0

using Newton-Raphson:

x \approx 2.35530 \dots

Apply long division:

\frac{x ^{3} - 3 x - 6}{x - 2.35530 \dots} = x^{2} + 2.35530 \dots x + 2.54744 \dots

x^{2} + 2.35530 \dots x + 2.54744 \dots \approx 0

Find one solution for

x^{2} + 2.35530 \dots x + 2.54744 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.35530 \dots

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

X^{3} - 3 X + 2 = 0

4 x^{3} + 12 x^{2} - 25 x - 75 = 0

x^{4} + 6 x^{3} + 14 x^{2} - 24 x - 72 = 0

4 m^{4} + 17 m^{2} + 4 = 0

What are the solutions to the equation x+1=x^3-2x-5 ?
The solutions to the equation x+1=x^3-2x-5 are x\approx 2.35530…
Find the zeros of x+1=x^3-2x-5
The zeros of x+1=x^3-2x-5 are x\approx 2.35530…