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

The solutions to the equation 2x^3-x^2+x-1=2x-1 are x=0,x=-1/2 ,x=1

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

The zeros of 2x^3-x^2+x-1=2x-1 are x=0,x=-1/2 ,x=1

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

x = 0, x = - \frac{1}{2}, x = 1

Decimal Notation

x = 0, x = - 0.5, x = 1

Solution steps

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

Move

1

to the right side

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

Move

2 x

to the left side

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

Factor

2 x^{3} - x^{2} - x : x (2 x + 1) (x - 1)

x (2 x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x + 1 = 0 or x - 1 = 0

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = - \frac{1}{2}, x = 1

x^{3} - 25 = 1 0^{2}

2 x^{3} + 12 - 5 = 0

x^{3} - 16 x^{2} + 79 x - 120 = 0

2 x^{3} - 7 x^{2} + 12 x + 8 = 0

k^{3} = 64

What are the solutions to the equation 2x^3-x^2+x-1=2x-1 ?
The solutions to the equation 2x^3-x^2+x-1=2x-1 are x=0,x=-1/2 ,x=1
Find the zeros of 2x^3-x^2+x-1=2x-1
The zeros of 2x^3-x^2+x-1=2x-1 are x=0,x=-1/2 ,x=1