X^+11x+24=0

1. The equation is in the form of \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 11 \), and \( c = 24 \).

2. To factorize, we need to find two numbers that multiply to \( ac = 24 \) and add to \( b = 11 \).

3. The numbers are \( 3 \) and \( 8 \) because \( 3 \times 8 = 24 \) and \( 3 + 8 = 11 \).

4. Factorize the quadratic equation:

(x + 3)(x + 8) = 0

5. Solve for \( x \):

x + 3 = 0 \quad \Rightarrow \quad x = -3

x + 8 = 0 \quad \Rightarrow \quad x = -8

*Therefore, the solution is:*

x = -3, -8