Final answer:
The equation (x+1)^2 = -4 is a quadratic equation with two real solutions.
Step-by-step explanation:
The equation (x+1)^2 = -4 is a quadratic equation. To determine the number of solutions, we can analyze the discriminant of the equation which is given by the formula b^2 - 4ac.
In this case, a = 1, b = 2, and c = -3. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution.
If the discriminant is less than zero, the equation has no real solutions. Plugging the values into the discriminant formula, we have 2^2 - 4(1)(-4) = 20 which is greater than zero.
Therefore, the equation has two real solutions.