How do you solve x3 plus 125 is equals to 0?

Answer 1

x^(3) + 125 = 0

Remember that 125 = 5^(3)

Hence

x^(3) + 5^(3) = 0

Factor

(x + 5) ( x^(2) - 5x + 25) = 0

So x = -5

&

x^(2) - 5x + 125 = 0

Apply Quadratic Eq'n

x = {--5 +/- sqrt[)=5)^(2) - 4(1)(125)]} / 2(1)

x = { 1 +/- sqrt[25 - 500]} / 2

x = { 1 +/- sqrt[-374] } / 2

This part remain unresolved because you cannot rake the square root of a negative number.

Hence x = -5 is the only result.

Answer 2

Realising that 125 is a perfect cube, this is actually pretty easy:

x3 + 125 = 0

x3 = -125

x = -5