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

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

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

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

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

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

Solution steps

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

Expand

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

- x^{3} + 3 x^{2} - 3 x + 1 = 8

Move

8

to the left side

- 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

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

(p^{8})^{2} = p^{10}

50 = 4 x^{3} - 44 x^{2} + 120 x

2 x^{3} + 6 x = 1

v^{3} + 1 = 0

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