To determine the number of real solutions for the quadratic equation \( 25x^2 + 60x + 36 = 0 \), we can use the discriminant method. The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \), where \( a = 25 \), \( b = 60 \), and \( c = 36 \).
The discriminant \( D \) is calculated using the formula:
\[ D = b^2 - 4ac \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ D = (60)^2 - 4(25)(36) \] \[ D = 3600 - 3600 \] \[ D = 0 \]
The discriminant \( D = 0 \) indicates that the quadratic equation has exactly one real solution (a repeated root).
Thus, the equation \( 25x^2 + 60x + 36 = 0 \) has 1 real solution.