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

The solutions to the equation (x-2)^3=-x+4 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2

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

The zeros of (x-2)^3=-x+4 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2

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

x = 3, x = \frac{3}{2} + i \frac{7}{2}, x = \frac{3}{2} - i \frac{7}{2}

Solution steps

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

Expand

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

x^{3} - 6 x^{2} + 12 x - 8 = - x + 4

Move

4

to the left side

x^{3} - 6 x^{2} + 12 x - 12 = - x

Move

x

to the left side

x^{3} - 6 x^{2} + 13 x - 12 = 0

Factor

x^{3} - 6 x^{2} + 13 x - 12 : (x - 3) (x^{2} - 3 x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 3 x + 4 = 0 : x = \frac{3}{2} + i \frac{7}{2}, x = \frac{3}{2} - i \frac{7}{2}

The solutions are

x = 3, x = \frac{3}{2} + i \frac{7}{2}, x = \frac{3}{2} - i \frac{7}{2}

220000 = 100000 \cdot (1 + x)^{3}

x, f = 10 + x^{3} f (27)

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

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

x, a = (2 x^{5} y^{3})^{3}

What are the solutions to the equation (x-2)^3=-x+4 ?
The solutions to the equation (x-2)^3=-x+4 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2
Find the zeros of (x-2)^3=-x+4
The zeros of (x-2)^3=-x+4 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2