Rewrite the equation by completing the square x^+11x+24=0

1. Start with the equation:

x^2 + 11x + 24 = 0

2. Isolate the constant term on one side:

x^2 + 11x = -24

3. Complete the square by adding and subtracting the square of half the coefficient of \( x \):

x^2 + 11x + \left(\frac{11}{2}\right)^2 = -24 + \left(\frac{11}{2}\right)^2

4. Simplify:

x^2 + 11x + \frac{121}{4} = -24 + \frac{121}{4}

5. Convert -24 to a fraction with a common denominator:

-24 = \frac{-96}{4}

6. Combine the fractions:

x^2 + 11x + \frac{121}{4} = \frac{-96}{4} + \frac{121}{4}

x^2 + 11x + \frac{121}{4} = \frac{25}{4}

7. Rewrite the left-hand side as a square:

\left(x + \frac{11}{2}\right)^2 = \frac{25}{4}

8. Isolate the perfect square term:

\left(x + \frac{11}{2}\right)^2 = \frac{25}{4}