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

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

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

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

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

x = - 1, x = - 1 + i, x = - 1 - i

Solution steps

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

Expand

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} + 2 x + 2 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} + 2 x + 2 = 0 : x = - 1 + i, x = - 1 - i

The solutions are

x = - 1, x = - 1 + i, x = - 1 - i

x^{3} + 25.3 x^{2} + 219.5 x + 660.1 = 0

x^{5} - 50 = 0

10750 = 5000 \cdot (1 + x)^{6}

x^{10} = x

x^{4} + 16 = 10 x^{2}

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