Question

`m2+14m+33=`?

Answer 1

`m^2+14m+33=(m+3)(m+11)`

`m=-3,-11`

Explanation:

Given:

`m^2+14m+33=`

If you are asking for the factorization, find two numbers that when added equal `14` and when multiplied equal `33`. The numbers `3` and `11` meet the requirements.

`m^2+14m+33=(m+3)(m+11)`

If you are asking to solve for `m`, set the equation equal to `0`.

`m^2+14m+33=0`

`(m+3)(m+11)=0`

Set each binomial equal to `0` and solve.

`m+3=0`

`m=-3`

`m+11=0`

`m=-11`

`m=-3,-11`

Answer 2

`m=-3` or `m=-11`

Explanation:

I'm assuming you want to solve

`m^2+14m+33=0`

To do so we may use the quadratic formula, but in this case there is a shorter, easier way.

Everytime you have an equation like

`x^2-sx+p=0`

you can solve it by looking for two numbers `x_1`, `x_2` such that `x_1+x_2=s` and `x_1x_2=p`

In this case, `s=-14` and `p=33`.

If we want two numbers to give `33` when multiplied, we can only choose `3` and `11` or `-3` and `-11`. Since we want the sum to be `-14`, the correct choice is `-3` and `-11`, which are the two solutions.