Find All Solutions to the Cubic Equation x³+1=0

In the given equation:

$x^3+1=0$The simplest and fastest way to find the number of its solutions,

will be simply to solve it, we will do this by moving terms to isolate the unknown, then we will take the cube root of both sides of the equation, while remembering that an odd root preserves the sign of the expression inside the root (meaning - the minus sign can be taken out of an odd root):

$x^3+1=0 \\ x^3=-1\hspace{6pt}\text{/}\sqrt[3]{\hspace{4pt}}\\ \downarrow\\ \sqrt[3]{x^3}=\sqrt[3]{-1}\\ x=-\sqrt[3]{1}\\ \boxed{x=-1}$meaning the given equation has a single solution,

therefore the correct answer is answer A.