To determine how many real solutions the quadratic equation \(25x^2 + 60x + 36 = 0\) has, we can use the discriminant of the quadratic formula. The discriminant \(D\) is given by:
\[ D = b^2 - 4ac \]
where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation \(ax^2 + bx + c = 0\).
In your equation:
- \(a = 25\)
- \(b = 60\)
- \(c = 36\)
Now, calculate the discriminant:
\[ D = (60)^2 - 4(25)(36) \] \[ D = 3600 - 3600 \] \[ D = 0 \]
The value of the discriminant \(D = 0\) indicates that there is exactly one real solution (or one repeated root) for the quadratic equation.
So, the answer is that the equation has 1 real solution.