We are given the quadratic equation [tex]\displaystyle{x^2=-5x[/tex].
Note that if x=0, both sides of the equation are equal to 0.
So x=0 is a solution.
For [tex]x\neq0[/tex], then we can divide both sides of the equation by x, and we get x=-5.
Thus, the solution set is {0, -5}.
Remark: another way to solve the equation is to take -5x to the left hand side:
[tex]\displaystyle{x^2+5x=0[/tex],
then we factorize x as
[tex]\displaystyle{x(x+5)=0[/tex].
Thus we see that x is either 0, or -5.
