What are the solutions to the equation 1/2 x^3+3x-4=-2 ?

The solutions to the equation 1/2 x^3+3x-4=-2 are x\approx 0.62581…

Find the zeros of 1/2 x^3+3x-4=-2

The zeros of 1/2 x^3+3x-4=-2 are x\approx 0.62581…

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\frac{1}{2} x^{3} + 3 x - 4 = - 2

x \approx 0.62581 \dots

Solution steps

\frac{1}{2} x^{3} + 3 x - 4 = - 2

Multiply both sides by

2

x^{3} + 6 x - 8 = - 4

Move

4

to the left side

x^{3} + 6 x - 4 = 0

Find one solution for

x^{3} + 6 x - 4 = 0

using Newton-Raphson:

x \approx 0.62581 \dots

Apply long division:

\frac{x ^{3} + 6 x - 4}{x - 0.62581 \dots} = x^{2} + 0.62581 \dots x + 6.39164 \dots

x^{2} + 0.62581 \dots x + 6.39164 \dots \approx 0

Find one solution for

x^{2} + 0.62581 \dots x + 6.39164 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.62581 \dots

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

(x + 2) (x^{2} - 1) = 0

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

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

x^{4} + 2 x^{3} + 4 x^{2} + 8 x + 16 = 0

What are the solutions to the equation 1/2 x^3+3x-4=-2 ?
The solutions to the equation 1/2 x^3+3x-4=-2 are x\approx 0.62581…
Find the zeros of 1/2 x^3+3x-4=-2
The zeros of 1/2 x^3+3x-4=-2 are x\approx 0.62581…