How do you factor 9x^2 + 6x + 1 = 12x?

1 Answer
May 4, 2018

x = 1/3

Explanation:

9x^2 + 6x + 1 = 12x

subtract 12x from both sides

9x^2 + 6x + 1 - 12x= 0

color(red)"6x - 12x"

9x^2 color(red)"- 6x" + 1 = 0


then my way that I use when the coefficient of x^2 not 1
that I multiply the constant by the coefficient of x^2 then I try to find two numbers that their product equals to the coefficient of x^2 and their sum equals to the coefficient of x.


like here for example

9x^2 - 6x + 1= 0

9*1=9

so the two numbers are -3 and -3

their product = 9 and their sum = -6

so then I put them in color(red)"-6x" place
9x^2 color(red)"- 3x - 3x" + 1= 0

the by grouping take the common factor

color(red)"9x^2 - 3x" color(blue)" - 3x + 1= 0"

3x(3x-1)-(3x-1)=0

so

(3x-1)(3x-1) = 0

(3x-1)^2=0

square root both sides

3x-1 = 0

add 1 to both sides

3x = 1

divide both sides by 3

x = 1/3