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

The solutions to the equation x^3=2x-3 are x\approx-1.89328…

Find the zeros of x^3=2x-3

The zeros of x^3=2x-3 are x\approx-1.89328…

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x^{3} = 2 x - 3

x \approx - 1.89328 \dots

Solution steps

x^{3} = 2 x - 3

Move

3

to the left side

x^{3} + 3 = 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.89328 \dots

Apply long division:

\frac{x ^{3} - 2 x + 3}{x + 1.89328 \dots} = x^{2} - 1.89328 \dots x + 1.58454 \dots

x^{2} - 1.89328 \dots x + 1.58454 \dots \approx 0

Find one solution for

x^{2} - 1.89328 \dots x + 1.58454 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.89328 \dots

x^{3} = 2 x + 4

x^{3} + 3 x^{2} - 4 x + 5 = 0

799675 = 524442 (1 + x)^{10}

6 x^{4} = 3072 x

(1 - x) (1 - x) (1 - x) + (1 - x) = 0

What are the solutions to the equation x^3=2x-3 ?
The solutions to the equation x^3=2x-3 are x\approx-1.89328…
Find the zeros of x^3=2x-3
The zeros of x^3=2x-3 are x\approx-1.89328…