What are the solutions to the equation 4x^3-2=2x+33-1 ?

The solutions to the equation 4x^3-2=2x+33-1 are x\approx 2.12245…

Find the zeros of 4x^3-2=2x+33-1

The zeros of 4x^3-2=2x+33-1 are x\approx 2.12245…

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4 x^{3} - 2 = 2 x + 33 - 1

x \approx 2.12245 \dots

Solution steps

4 x^{3} - 2 = 2 x + 33 - 1

Refine

4 x^{3} - 2 = 2 x + 32

Move

32

to the left side

4 x^{3} - 34 = 2 x

Move

2 x

to the left side

4 x^{3} - 34 - 2 x = 0

Write in the standard form

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

4 x^{3} - 2 x - 34 = 0

Find one solution for

4 x^{3} - 2 x - 34 = 0

using Newton-Raphson:

x \approx 2.12245 \dots

Apply long division:

\frac{4 x ^{3} - 2 x - 34}{x - 2.12245 \dots} = 4 x^{2} + 8.48980 \dots x + 16.01920 \dots

4 x^{2} + 8.48980 \dots x + 16.01920 \dots \approx 0

Find one solution for

4 x^{2} + 8.48980 \dots x + 16.01920 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.12245 \dots

y - y^{9} = 0

x^{4} - 48 x^{2} + 512 = 0

(2 x - 3) (x^{2} - 16) = 0

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

x^{6} - 13 x^{3} + 42 = 0

What are the solutions to the equation 4x^3-2=2x+33-1 ?
The solutions to the equation 4x^3-2=2x+33-1 are x\approx 2.12245…
Find the zeros of 4x^3-2=2x+33-1
The zeros of 4x^3-2=2x+33-1 are x\approx 2.12245…