What are the solutions to the equation (x+1)^3=-27 ?

The solutions to the equation (x+1)^3=-27 are x=-4,x= 1/2+i(3sqrt(3))/2 ,x= 1/2-i(3sqrt(3))/2

Find the zeros of (x+1)^3=-27

The zeros of (x+1)^3=-27 are x=-4,x= 1/2+i(3sqrt(3))/2 ,x= 1/2-i(3sqrt(3))/2

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(x + 1)^{3} = - 27

x = - 4, x = \frac{1}{2} + i \frac{3 3}{2}, x = \frac{1}{2} - i \frac{3 3}{2}

Solution steps

(x + 1)^{3} = - 27

Expand

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

x^{3} + 3 x^{2} + 3 x + 1 = - 27

Move

27

to the left side

x^{3} + 3 x^{2} + 3 x + 28 = 0

Factor

x^{3} + 3 x^{2} + 3 x + 28 : (x + 4) (x^{2} - x + 7)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 4 = 0 : x = - 4

Solve

x^{2} - x + 7 = 0 : x = \frac{1}{2} + i \frac{3 3}{2}, x = \frac{1}{2} - i \frac{3 3}{2}

The solutions are

x = - 4, x = \frac{1}{2} + i \frac{3 3}{2}, x = \frac{1}{2} - i \frac{3 3}{2}

x^{4} - 4 x^{2} - 21 = 0

16 x^{3} - 32 x^{2} - 4 x + 8 = 0

- λ^{3} + 4 λ^{2} - 3 λ = 0

x (x - 5) (x - 7) = x (7 - x)

x^{3} - 5 x^{2} - 25 x = - 125

What are the solutions to the equation (x+1)^3=-27 ?
The solutions to the equation (x+1)^3=-27 are x=-4,x= 1/2+i(3sqrt(3))/2 ,x= 1/2-i(3sqrt(3))/2
Find the zeros of (x+1)^3=-27
The zeros of (x+1)^3=-27 are x=-4,x= 1/2+i(3sqrt(3))/2 ,x= 1/2-i(3sqrt(3))/2