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

1 Answer
Aug 16, 2015

Answer:

The solutions are:

#color(blue)(x=1#
#color(blue)(x=-7#

Explanation:

# x^2+6x+2=9#
# x^2+6x+2-9=0#
# x^2+6x-7=0#

We can Split the Middle Term of this expression to factorise it and then we 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*-7 = -7#
and
#N_1 +N_2 = b = 6#

After trying out a few numbers we get #N_1 = 7# and #N_2 =-1#
#7*(-1) = -7#, and #7+(-1)= 6#

# x^2+6x-7 = x^2+7x-1x-7 #
#x(x+7)(-1(x+7)=0#
#(x-1)(x+7)=0#
Now we equate the factors to zero and find the solutions.

#x-1=0,color(blue)(x=1#
#x+7=0,color(blue)(x=-7#