What are the solutions to the equation (x-1)^3+8=0 ?

The solutions to the equation (x-1)^3+8=0 are x=-1,x=2+sqrt(3)i,x=2-sqrt(3)i

Find the zeros of (x-1)^3+8=0

The zeros of (x-1)^3+8=0 are x=-1,x=2+sqrt(3)i,x=2-sqrt(3)i

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(x - 1)^{3} + 8 = 0

x = - 1, x = 2 + 3 i, x = 2 - 3 i

Solution steps

(x - 1)^{3} + 8 = 0

Expand

(x - 1)^{3} + 8 : x^{3} - 3 x^{2} + 3 x + 7

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

Factor

x^{3} - 3 x^{2} + 3 x + 7 : (x + 1) (x^{2} - 4 x + 7)

(x + 1) (x^{2} - 4 x + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - 4 x + 7 = 0

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

x = - 1, x = 2 + 3 i, x = 2 - 3 i

8 x^{3} - 14 x^{2} + 7 x - 1 = 0

x^{4} - 10 x^{2} = - 9

z^{3} + 64 = 0

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

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

What are the solutions to the equation (x-1)^3+8=0 ?
The solutions to the equation (x-1)^3+8=0 are x=-1,x=2+sqrt(3)i,x=2-sqrt(3)i
Find the zeros of (x-1)^3+8=0
The zeros of (x-1)^3+8=0 are x=-1,x=2+sqrt(3)i,x=2-sqrt(3)i