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

The solutions to the equation 4x^3-1=2x^2-2x are x= 1/2 ,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i

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

The zeros of 4x^3-1=2x^2-2x are x= 1/2 ,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i

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

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

Solution steps

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

Move

2 x

to the left side

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

Move

2 x^{2}

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

The solutions are

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

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

x (x + 4) (x - 1) = 0

x^{3} - 49 x + 120 = 0

- x^{3} + 12 x^{2} - 21 x + 10 = 0

27 x^{3} - 512 = 0

What are the solutions to the equation 4x^3-1=2x^2-2x ?
The solutions to the equation 4x^3-1=2x^2-2x are x= 1/2 ,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i
Find the zeros of 4x^3-1=2x^2-2x
The zeros of 4x^3-1=2x^2-2x are x= 1/2 ,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i