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

1 Answer
Oct 8, 2015

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 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.