What are the solutions to the equation (x-5)^3+12=-15 ?

The solutions to the equation (x-5)^3+12=-15 are x=2,x= 13/2+i(3sqrt(3))/2 ,x= 13/2-i(3sqrt(3))/2

Find the zeros of (x-5)^3+12=-15

The zeros of (x-5)^3+12=-15 are x=2,x= 13/2+i(3sqrt(3))/2 ,x= 13/2-i(3sqrt(3))/2

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(x - 5)^{3} + 12 = - 15

x = 2, x = \frac{13}{2} + i \frac{3 3}{2}, x = \frac{13}{2} - i \frac{3 3}{2}

Solution steps

(x - 5)^{3} + 12 = - 15

Expand

(x - 5)^{3} + 12 : x^{3} - 15 x^{2} + 75 x - 113

x^{3} - 15 x^{2} + 75 x - 113 = - 15

Move

15

to the left side

x^{3} - 15 x^{2} + 75 x - 98 = 0

Factor

x^{3} - 15 x^{2} + 75 x - 98 : (x - 2) (x^{2} - 13 x + 49)

(x - 2) (x^{2} - 13 x + 49) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} - 13 x + 49 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 13 x + 49 = 0 : x = \frac{13}{2} + i \frac{3 3}{2}, x = \frac{13}{2} - i \frac{3 3}{2}

The solutions are

x = 2, x = \frac{13}{2} + i \frac{3 3}{2}, x = \frac{13}{2} - i \frac{3 3}{2}

m^{4} + 2 m^{3} + 11 m^{2} + 2 m + 10 = 0

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

48 x + 10 x^{2} - 2 x^{3} = 0

x, x^{4} = 16

2 = 3 x^{5} + x - 2

What are the solutions to the equation (x-5)^3+12=-15 ?
The solutions to the equation (x-5)^3+12=-15 are x=2,x= 13/2+i(3sqrt(3))/2 ,x= 13/2-i(3sqrt(3))/2
Find the zeros of (x-5)^3+12=-15
The zeros of (x-5)^3+12=-15 are x=2,x= 13/2+i(3sqrt(3))/2 ,x= 13/2-i(3sqrt(3))/2