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

The solutions to the equation 2x^2-3x+2=x^3+4x+4-4 are x\approx 0.30874…

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

The zeros of 2x^2-3x+2=x^3+4x+4-4 are x\approx 0.30874…

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

x \approx 0.30874 \dots

Solution steps

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

Refine

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

Switch sides

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

Move

2

to the left side

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

Move

3 x

to the left side

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

Move

2 x^{2}

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.30874 \dots

Apply long division:

\frac{x ^{3} - 2 x ^{2} + 7 x - 2}{x - 0.30874 \dots} = x^{2} - 1.69125 \dots x + 6.47783 \dots

x^{2} - 1.69125 \dots x + 6.47783 \dots \approx 0

Find one solution for

x^{2} - 1.69125 \dots x + 6.47783 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.30874 \dots

r^{3} - 1 = 0

x^{3} - x^{2} + x + 1 = 0

3 x^{3} - x^{2} - 48 x + 16 = 0

x^{3} - 11 x^{2} + 36 x - 45 = 0

x^{3} - 13 x = 0

What are the solutions to the equation 2x^2-3x+2=x^3+4x+4-4 ?
The solutions to the equation 2x^2-3x+2=x^3+4x+4-4 are x\approx 0.30874…
Find the zeros of 2x^2-3x+2=x^3+4x+4-4
The zeros of 2x^2-3x+2=x^3+4x+4-4 are x\approx 0.30874…