Question 668772
f(x) = x^3 + 343 = x^3 + 7^3 <--- important to recognize this since for (a^3 + b^3) = (a+b)(a^2-ab+b^2) where a=x and b = 7

(x+7)(x^2-7x+49)

{{{highlight(x = -7)}}}

(x^2-7x+49) use quadratic formula

{{{x = (7 +- sqrt(49-4*49*1))/(2)}}}

{{{x = (7 +- sqrt(49-196))/2}}}

{{{x = (7 +- sqrt(-147))/2}}}

{{{x = (7 +- i*sqrt(3*49))/2}}}

{{{x = highlight((7 +- 7i*sqrt(3))/2)}}}