How do you solve #x^2 + 6x + 9 = 0# by factoring?

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Answer 1 · 2015-10-08T14:44:22

#color(blue)(x=-3#

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

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

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+color(blue)(6x)+9 = x^2 +color(blue)(3x +3x)+9#

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

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

We now equate the factor to zero to obtain the solution (both factors are equal here).
#x+3=0#
#color(blue)(x=-3# is the solution.