[tex]~~~~~8-x^3 = 0\\\\\implies 2^3 -x^3 = 0\\\\\implies (2-x)(2^2 + 2x +x^2) = 0\\\\\implies (2-x) (4+2x +x^2) = 0\\\\\implies 2-x = 0~~~~~~~~~~~;[\text{The roots of }~ x^2 +2x +4 =0~ \text{ are complex}].\\\\\implies x = 2\\\\\text{Hence,}~ x =2~ \text{ is the only real solution.}[/tex]
