To solve the quadratic equation \( d^2 - 23d - 24 = 0 \), we can use the quadratic formula:
\[ d = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, \( a = 1 \), \( b = -23 \), and \( c = -24 \).
First, we calculate the discriminant (\( b^2 - 4ac \)):
\[ b^2 = (-23)^2 = 529 \] \[ 4ac = 4 \cdot 1 \cdot (-24) = -96 \] \[ b^2 - 4ac = 529 - (-96) = 529 + 96 = 625 \]
Now plug the values into the quadratic formula:
\[ d = \frac{-(-23) \pm \sqrt{625}}{2 \cdot 1} = \frac{23 \pm 25}{2} \]
This gives us two possible solutions:
\[ d = \frac{23 + 25}{2} = \frac{48}{2} = 24 \] 2. \[ d = \frac{23 - 25}{2} = \frac{-2}{2} = -1 \]
Thus, the solutions are \( d = 24 \) and \( d = -1 \).
The final answer is:
\[ d = 24, -1 \]