Question

How do you factor and solve `x^2+ 15x= -36`?

Answer 1

`x = -3`
and
`x=-12`

Explanation:

To solve `x^2+15x=-36`

We begin by setting the equation equal to zero.
`x^2+15x+36=cancel(-36) cancel(+36)`

`x^2+15x+36=0`

Now find the factors of 36
`1 and 36`
`2 and18`
`3and12`
`4and9`
`6and6`

Since the second sign of the trinomial is `+` we must add the factors to get the middle term 15.
Since the first sign of the trinomial is `+` we know the factor must both be `+`

So the factors are `3 and 12`

Now factor the trinomial

`(x+3)(x+12)=0`

Set each factor equal to zero and solve.

`x+3=0`

`xcancel(+3) cancel(-3)=0-3`

`x=-3`

and
`x+12=0`

`xcancel(+12) cancel(-12)=0-12`

`x=-12`