Answer to Question #252165 in Algebra for Jayson

Question

X2 + 6X + 9 =0

Answer 1

Given a general quadratic expression

ax²+bx+c

The coefficient of the middle term "b" can be split into two terms

N₁ and N₂

Such that N₁ .N₂ =a.c

And N₁ +N₂ =b

Applying this in the equation

X² +6x+9=0

6 is split into N₁ and N₂

Such that N₁ .N₂ = 1.9=9

N₁ +N₂=6

Possible factors of 9 are

1and 9

3 and 3

Factors 3 and 3 satisfies the condition

3.3=9

3+3=6

Therefore x²+3x+3x+9=0

Paring the terms and factorizing

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

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

Therefore either x+3=0 or x+3=0

(Both factors are equal)

Therefore

x= -3