Solve the equation x ^ 2 = -x. If your equation has more than one root, indicate the smaller one in your answer.

x ^ 2 = -x;
move x to the left side of the equation:
x ^ 2 + x = 0;
put x out of brackets:
x (x + 1) = 0;
the product is zero when at least one of the factors is zero, while the other makes sense, that is
or x = 0 or x + 1 = 0;
x = 0 or x = -1.
-1 <0, that is, write one root equal to -1 in the answer.
Answer: -1.