What are the solutions to the equation (2x-1)^3-4x(2x-3)=5 ?

The solutions to the equation (2x-1)^3-4x(2x-3)=5 are x=1,x= 3/4+i(sqrt(3))/4 ,x= 3/4-i(sqrt(3))/4

Find the zeros of (2x-1)^3-4x(2x-3)=5

The zeros of (2x-1)^3-4x(2x-3)=5 are x=1,x= 3/4+i(sqrt(3))/4 ,x= 3/4-i(sqrt(3))/4

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(2 x - 1)^{3} - 4 x (2 x - 3) = 5

x = 1, x = \frac{3}{4} + i \frac{3}{4}, x = \frac{3}{4} - i \frac{3}{4}

Solution steps

(2 x - 1)^{3} - 4 x (2 x - 3) = 5

Expand

(2 x - 1)^{3} - 4 x (2 x - 3) : 8 x^{3} - 20 x^{2} + 18 x - 1

8 x^{3} - 20 x^{2} + 18 x - 1 = 5

Move

5

to the left side

8 x^{3} - 20 x^{2} + 18 x - 6 = 0

Factor

8 x^{3} - 20 x^{2} + 18 x - 6 : 2 (x - 1) (4 x^{2} - 6 x + 3)

2 (x - 1) (4 x^{2} - 6 x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 4 x^{2} - 6 x + 3 = 0

Solve

x - 1 = 0 : x = 1

Solve

4 x^{2} - 6 x + 3 = 0 : x = \frac{3}{4} + i \frac{3}{4}, x = \frac{3}{4} - i \frac{3}{4}

The solutions are

x = 1, x = \frac{3}{4} + i \frac{3}{4}, x = \frac{3}{4} - i \frac{3}{4}

a, a^{5} 4^{- 2} = 2

y^{3} = - 64

x^{3} = 243

y^{3} = - 27

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

What are the solutions to the equation (2x-1)^3-4x(2x-3)=5 ?
The solutions to the equation (2x-1)^3-4x(2x-3)=5 are x=1,x= 3/4+i(sqrt(3))/4 ,x= 3/4-i(sqrt(3))/4
Find the zeros of (2x-1)^3-4x(2x-3)=5
The zeros of (2x-1)^3-4x(2x-3)=5 are x=1,x= 3/4+i(sqrt(3))/4 ,x= 3/4-i(sqrt(3))/4