Question

How do you solve `x^2+5x+6=0` by factoring?

Answer 1

`x=-3" or "x=-2`

Explanation:

`"the factors of "+6" which sum to "+5"`
`"are "+3" and "+2`

`(x+3)(x+2)=0`

`"equate each factor to zero and solve for x"`

`x+3=0rArrx=-3`

`x+2=0rArrx=-2`

Answer 2

`x=-2` or `x=-3`

Explanation:

Completing the square

`x^2+2*5/2x+25/4+6-25/4=0`

we get

`(x+5/2)^2-1/4=0`

using that `a^2-b^2=(a+b)(a-b)`

we get
`(x+5/2-1/2)(x+5/2+1/2)=0`

so `(x+2)(x+3)=0`

we get `x=-2` or `x=-3`

Answer 3

`x=-2` and `x=-3`

Explanation:

Let's do a little thought experiment:

What two numbers sum to the middle term, and have a product of the last term?

After some trial and error, we arrive at `2` and `3`. This means we can factor this as

`(x+2)(x+3)=0`

Next, we can set both factors equal to zero to get

`x=-2` and `x=-3`

Hope this helps!