Question

1. $x^2 + 5x - 24 = 0$

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to $-24$ and add up to $5$. The numbers are $8$ and $-3$ since $8\times(-3)= -24$ and $8 + (-3)=5$. So we can factor the equation as:
$$x^{2}+5x - 24=(x + 8)(x - 3)=0$$

Step2: Solve for x

Set each factor equal to zero:

• For $x + 8 = 0$, we get $x=-8$.
• For $x - 3 = 0$, we get $x = 3$.

Answer:

The solutions are $x = -8$ and $x = 3$.