What are the real or imaginary solutions of the polynomial equation? 27x^3+125=0

I have no idea how to do this

Question

What are the real or imaginary solutions of the polynomial equation? 27x^3+125=0 

I have no idea how to do this

radar · Answer

It is the sum of two cubes:$$(3x)^{3} + 5^{3}$$

anonymous · Answer

What does that mean? I need help figuring out how to do this please

radar · Answer

It means that it is factorable and may be solved$$a ^{3}+b ^{3}= (a + b)(a ^{2}-ab + b ^{2}$$

radar · Answer

a=3x, b=5
(3x + 5)(9x^2 - 15x + 25)=0 thus
3x+5 = 0, x=-5/3 would be one answer, there will be 2 more solutions when you solve the quadratic.

radar · Answer

The other 2 solution are complex values, use the quadratic formula to solve the quadratic