Which are the solutions of the quadratic equation? x2 = –5x – 3 –5, 0 5, 0

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.