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

1 Answer
Jun 7, 2016

Answer:

#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#