What are the solutions to the equation x^3=3x+6 ?

The solutions to the equation x^3=3x+6 are x\approx 2.35530…

Find the zeros of x^3=3x+6

The zeros of x^3=3x+6 are x\approx 2.35530…

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x^{3} = 3 x + 6

x \approx 2.35530 \dots

Solution steps

x^{3} = 3 x + 6

Move

6

to the left side

x^{3} - 6 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

17994 = 1624 \cdot (1 + x)^{12}

8 x^{15} + 7 = - 3

x, 2 x^{3} - 3 x = - 10

40 w^{3} - 3 w^{2} - w = 0

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

What are the solutions to the equation x^3=3x+6 ?
The solutions to the equation x^3=3x+6 are x\approx 2.35530…
Find the zeros of x^3=3x+6
The zeros of x^3=3x+6 are x\approx 2.35530…