How many real solutions does the following quadratic equation have?
25x^2 + 60x + 36 = 0
To find the number of real solutions of the quadratic equation 25x^2 + 60x + 36 = 0, we can use the discriminant. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
For this quadratic equation, a = 25, b = 60, and c = 36. Plugging these values into the discriminant formula, we get:
b^2 - 4ac = (60)^2 - 4(25)(36) = 3600 - 3600 = 0.
Since the discriminant is equal to 0, the quadratic equation has exactly one real solution.