What are the solutions to the equation x^3+27+3(x+3)=0 ?

The solutions to the equation x^3+27+3(x+3)=0 are x=-3,x= 3/2+i(sqrt(39))/2 ,x= 3/2-i(sqrt(39))/2

Find the zeros of x^3+27+3(x+3)=0

The zeros of x^3+27+3(x+3)=0 are x=-3,x= 3/2+i(sqrt(39))/2 ,x= 3/2-i(sqrt(39))/2

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x^{3} + 27 + 3 (x + 3) = 0

x = - 3, x = \frac{3}{2} + i \frac{39}{2}, x = \frac{3}{2} - i \frac{39}{2}

Solution steps

x^{3} + 27 + 3 (x + 3) = 0

Expand

x^{3} + 27 + 3 (x + 3) : x^{3} + 3 x + 36

x^{3} + 3 x + 36 = 0

Factor

x^{3} + 3 x + 36 : (x + 3) (x^{2} - 3 x + 12)

(x + 3) (x^{2} - 3 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x^{2} - 3 x + 12 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x^{2} - 3 x + 12 = 0 : x = \frac{3}{2} + i \frac{39}{2}, x = \frac{3}{2} - i \frac{39}{2}

The solutions are

x = - 3, x = \frac{3}{2} + i \frac{39}{2}, x = \frac{3}{2} - i \frac{39}{2}

(x) = 2 x^{3} - 1500

x^{4} - (x - 0.5)^{4} = 1 0^{4}

0 = x^{3} - x + 3

x^{10} = 1024

x, y^{3} + 7 y = x^{3}

What are the solutions to the equation x^3+27+3(x+3)=0 ?
The solutions to the equation x^3+27+3(x+3)=0 are x=-3,x= 3/2+i(sqrt(39))/2 ,x= 3/2-i(sqrt(39))/2
Find the zeros of x^3+27+3(x+3)=0
The zeros of x^3+27+3(x+3)=0 are x=-3,x= 3/2+i(sqrt(39))/2 ,x= 3/2-i(sqrt(39))/2