What are the solutions to the equation (x-2)^3=-125 ?

The solutions to the equation (x-2)^3=-125 are x=-3,x= 9/2+i(5sqrt(3))/2 ,x= 9/2-i(5sqrt(3))/2

Find the zeros of (x-2)^3=-125

The zeros of (x-2)^3=-125 are x=-3,x= 9/2+i(5sqrt(3))/2 ,x= 9/2-i(5sqrt(3))/2

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(x - 2)^{3} = - 125

x = - 3, x = \frac{9}{2} + i \frac{5 3}{2}, x = \frac{9}{2} - i \frac{5 3}{2}

Solution steps

(x - 2)^{3} = - 125

Expand

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

x^{3} - 6 x^{2} + 12 x - 8 = - 125

Move

125

to the left side

x^{3} - 6 x^{2} + 12 x + 117 = 0

Factor

x^{3} - 6 x^{2} + 12 x + 117 : (x + 3) (x^{2} - 9 x + 39)

(x + 3) (x^{2} - 9 x + 39) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x^{2} - 9 x + 39 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x^{2} - 9 x + 39 = 0 : x = \frac{9}{2} + i \frac{5 3}{2}, x = \frac{9}{2} - i \frac{5 3}{2}

The solutions are

x = - 3, x = \frac{9}{2} + i \frac{5 3}{2}, x = \frac{9}{2} - i \frac{5 3}{2}

4 x^{3} - 6 x^{2} = 10 x - 15

- 2 x (x^{2} - 5) (x^{2} + 1) = 0

x (x^{2} - 3)^{3} - 2 = 1785

\frac{3}{16} = 3 r^{4}

x^{4} - 7 x^{2} - 5 = 0

What are the solutions to the equation (x-2)^3=-125 ?
The solutions to the equation (x-2)^3=-125 are x=-3,x= 9/2+i(5sqrt(3))/2 ,x= 9/2-i(5sqrt(3))/2
Find the zeros of (x-2)^3=-125
The zeros of (x-2)^3=-125 are x=-3,x= 9/2+i(5sqrt(3))/2 ,x= 9/2-i(5sqrt(3))/2