To solve the quadratic equation \( w^2 + 24w - 25 = 0 \), we can use the quadratic formula:
\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, \( a = 1 \), \( b = 24 \), and \( c = -25 \).
First, we calculate the discriminant (\( b^2 - 4ac \)):
\[ b^2 - 4ac = 24^2 - 4 \cdot 1 \cdot (-25) = 576 + 100 = 676 \]
Next, we find the square root of the discriminant:
\[ \sqrt{676} = 26 \]
Now, we can apply the quadratic formula:
\[ w = \frac{-24 \pm 26}{2 \cdot 1} \]
This gives us two potential solutions:
- \( w = \frac{-24 + 26}{2} = \frac{2}{2} = 1 \)
- \( w = \frac{-24 - 26}{2} = \frac{-50}{2} = -25 \)
Thus, the solutions to the equation \( w^2 + 24w - 25 = 0 \) are:
\[ w = 1 \quad \text{and} \quad w = -25 \]