The problem is to find the roots of the quadratic equation $x^2 + 9x + 14 = 0$.

1. Problem Description

The problem is to find the roots of the quadratic equation $x^2 + 9x + 14 = 0$.

2. Solution Steps

We need to solve the quadratic equation $x^2 + 9x + 14 = 0$. We can solve this by factoring. We look for two numbers that multiply to 14 and add to

9. The numbers 2 and 7 satisfy these conditions, since $2 \cdot 7 = 14$ and $2 + 7 = 9$.

Therefore, we can factor the quadratic equation as:

$(x+2)(x+7)=0$

To find the roots, we set each factor equal to zero:

$x+2 = 0$ or $x+7 = 0$

Solving for $x$ in each case, we have:

$x = -2$ or $x = -7$

3. Final Answer

The solutions to the quadratic equation $x^2 + 9x + 14 = 0$ are $x = -2$ and $x = -7$.