Question

x² + 9x + 14 = 0

Explanation:

Step1: Factor the quadratic trinomial

Find two numbers that multiply to $14$ and add to $9$ (these are $2$ and $7$), so rewrite the equation:
$x^2 + 2x + 7x + 14 = 0$
Group and factor:
$x(x+2) + 7(x+2) = 0$
$(x+2)(x+7) = 0$

Step2: Solve for $x$ using zero product property

Set each factor equal to 0:
$x+2=0$ or $x+7=0$

Answer:

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