How do you solve #x^2+6x=-9# by factoring?

1 Answer
Aug 16, 2015

Answer:

The solutions is #color(blue)(x=-3#

Explanation:

# x^2+6x+9=0 #

We can Split the Middle Term of this expression to factorise it and thereby find the 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*9 = 9#
AND
#N_1 +N_2 = b = 6#
After trying out a few numbers we get #N_1 = 3# and #N_2 =3#
#3*3 = 9# and #3+3= 6#

# x^2+6x+9=x^2+3x+3x+9#

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

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

Now we equate the factors to zero and find the solutions.
#x+3 =0, color(blue)(x=-3#

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