Show that the statement $p:$ "If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$" is true by the direct method.

(N/A) The statement $p$ is: "If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$."
Let $q$ be the statement: "$x$ is a real number such that $x^{3}+4x=0$."
Let $r$ be the statement: "$x$ is $0$."
To prove $p$ is true by the direct method,we assume $q$ is true and show that $r$ must be true.
Assume $q$ is true,so $x^{3}+4x=0$.
Factoring the equation,we get $x(x^{2}+4)=0$.
This implies $x=0$ or $x^{2}+4=0$.
Since $x$ is a real number,$x^{2} \geq 0$,which means $x^{2}+4 \geq 4$.
Therefore,$x^{2}+4$ cannot be $0$ for any real number $x$.
Thus,the only possibility is $x=0$.
Since we have shown that $q$ implies $r$,the statement $p$ is true.