How do you solve #x^2+ 15x= -36# by factoring?

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Answer 1 · 2015-08-23T11:20:50

The solutions are
#color(blue)(x=-3#
# color(blue)(x=-12#

#x^2+15x=−36 #
#x^2+15x+36=0 #

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*36 =36#
AND
#N_1 +N_2 = b = 15#
After trying out a few numbers we get #N_1 = 12# and #N_2 =3#
#12*3 = 36#, and #12+3=15#

#x^2+15x+36=x^2+12x +3x+36 #

#=x(x+12) +3(x+12) #

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

Now we equate the factors to zero

#x+3=0, color(blue)(x=-3#
#x+12=0, color(blue)(x=-12#