Algebra 2

What are the real and complex solutions of the polynomial equation?

27x^3 + 125 = 0
I already got the real solution x = -5/3, I just need to figure out how to find the complex solution. Any help?

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  1. you have the sum of two cubes, so it factors into

    (3x+5)((3x)^2-(3x)(5)+5^2)
    = (3x+5)(9x^2-15x+25)

    It's easy to check that the quadratic has no real solutions. Just use the quadratic formula, learned long ago in Algebra I...

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