What are the solutions to the equation (x-2)^3=-8 ?

The solutions to the equation (x-2)^3=-8 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i

Find the zeros of (x-2)^3=-8

The zeros of (x-2)^3=-8 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i

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(x - 2)^{3} = - 8

x = 0, x = 3 + 3 i, x = 3 - 3 i

Solution steps

(x - 2)^{3} = - 8

Expand

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

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

Move

8

to the left side

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

Factor

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

x (x^{2} - 6 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 6 x + 12 = 0

Solve

x^{2} - 6 x + 12 = 0 : x = 3 + 3 i, x = 3 - 3 i

The solutions are

x = 0, x = 3 + 3 i, x = 3 - 3 i

(x - 1) (x + 1) (x + 3) (x + 5) + 15 = 0

n^{100} = 2

60 x^{3} - 22 x^{2} - 4 x = 0

x^{3} - 7 x^{2} + 8 x + 10 = 0

x^{4} - 8 x^{9} - 9 = 0

What are the solutions to the equation (x-2)^3=-8 ?
The solutions to the equation (x-2)^3=-8 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i
Find the zeros of (x-2)^3=-8
The zeros of (x-2)^3=-8 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i