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

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

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

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

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

x = - 3, x = 3 i, x = - 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 + 9 = 0

Factor

x^{3} + 3 x^{2} + 3 x + 9 : (x + 3) (x^{2} + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 3 = 0 : x = - 3

Solve

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

The solutions are

x = - 3, x = 3 i, x = - 3 i

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

2 x^{3} - 4 x^{2} - 7 x = - x^{2} + x + 3

x^{4} - 14 x^{2} + 49 = 0

x^{6} - 23 x^{4} + 4 x^{2} = 0

y^{3} + 3 y^{2} = 4 y + 12

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