The solutions to the quadratic equation q^2 + q = 0 are q = 0 and q = -1.
To solve the quadratic equation q^2 + q = 0, we can factor out q:
q(q + 1) = 0
Now, set each factor equal to zero and solve for q:
q = 0
q + 1 = 0
From the first equation, q = 0. From the second equation, q = -1.
Therefore, the solutions to the quadratic equation q^2 + q = 0 are q = 0 and q = -1.