How can i find the complex roots of 125x^3+343. explain your steps

First we assume that this is equal to zero

so what we notice is this is a sum of 2 perfect cube

recall that
a^3+b^3=(a+b)(a^2-ab+b^2)

125x^3+343=
(5x)³+(7)³=(5x+7)(25x²-35x+49)

now solve the part in second parenthasees because we can see that the first parenthasees (5x+7) is going to have a real root

remember quadratic formula

for ax^2+bx+c=0
x=
a=25
b=-35
c=49

x=
x=
x=
x=
x=
x=
x=

the comlex roots are

x= and

Aand b are correctly balanced reactions. they have the same number of atoms in both sides of the reaction