Question

solve for m.
$m^2 + 13m + 22 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form.
if there are multiple solutions, separate them with commas.
$m = $

Explanation:

Step1: Factor the quadratic trinomial

We find two numbers that multiply to $22$ and add to $13$: $11$ and $2$.
$m^2 + 13m + 22 = (m + 11)(m + 2) = 0$

Step2: Set each factor to zero

Apply the zero product property: if $ab=0$, then $a=0$ or $b=0$.
$m + 11 = 0$ or $m + 2 = 0$

Step3: Solve for $m$ in each equation

For $m + 11 = 0$: $m = -11$
For $m + 2 = 0$: $m = -2$

Answer:

$m = -11, -2$