What are the solutions to the equation (x+6)^3=-27 ?

The solutions to the equation (x+6)^3=-27 are x=-9,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2

Find the zeros of (x+6)^3=-27

The zeros of (x+6)^3=-27 are x=-9,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2

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(x + 6)^{3} = - 27

x = - 9, x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

Solution steps

(x + 6)^{3} = - 27

Expand

(x + 6)^{3} : x^{3} + 18 x^{2} + 108 x + 216

x^{3} + 18 x^{2} + 108 x + 216 = - 27

Move

27

to the left side

x^{3} + 18 x^{2} + 108 x + 243 = 0

Factor

x^{3} + 18 x^{2} + 108 x + 243 : (x + 9) (x^{2} + 9 x + 27)

(x + 9) (x^{2} + 9 x + 27) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 9 = 0 or x^{2} + 9 x + 27 = 0

Solve

x + 9 = 0 : x = - 9

Solve

x^{2} + 9 x + 27 = 0 : x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

The solutions are

x = - 9, x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

z^{4} + 4 z^{2} + 16 = 0

x^{4} - 29 x^{2} + 100 = 0

z^{3} = 27

x^{4} - 4 x^{3} + x^{2} + 4 x + 1 = 0

- 7 x^{2} - 16 x + 112 - x^{3} = 0

What are the solutions to the equation (x+6)^3=-27 ?
The solutions to the equation (x+6)^3=-27 are x=-9,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2
Find the zeros of (x+6)^3=-27
The zeros of (x+6)^3=-27 are x=-9,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2