How would you solve 9x^2+9x+2=0 by factoring? I am stuck :(

Question

campbell_st · Answer

well do it this way... works every time

for a quadratic in the form

$$ax^2 + bx + c $$

multiply a and c    

so in your question 9 x 2 = 18

now find the factors of 18 that add to b... or in your question 9

then the solution is

(ax + factor 1)(ax + factor 2)
--------------------------
                     a

in you question its 

(9x + factor 1)(9x + factor 2)
--------------------------
                   9

you'll find that each binomial will have common factors that cancel with the denominator

campbell_st · Answer

so 1st find the factors

dangerousjesse · Answer

Solve for x over the real numbers:
$9 x^2+9 x+2 = 0$
Factor the left hand side.
The left hand side factors into a product with two terms:
$(3 x+1) (3 x+2) = 0$
Solve each term in the product separately.
Split into two equations:
$3 x+1 = 0$ or $3 x+2 = 0$
Look at the first equation:  Isolate terms with x to the left hand side.
Subtract 1 from both sides:
$3 x = -1$ or $3 x+2 = 0$
Solve for x.
Divide both sides by 3:
$x = \frac{-1}{3}$ or $3 x+2 = 0$
Look at the second equation:  Isolate terms with x to the left hand side.
Subtract 2 from both sides:
$x = \frac{-1}{3}$ or $3 x = -2$
Solve for x.
Divide both sides by 3...

anonymous · Answer

LOL, I'm a real idiot. I was wondering how any factors of 2 could be 9 but I just realized that there are 3x and not x. Thanks to both of you

anonymous · Answer

I didn't really get campbell_st's explanation

campbell_st · Answer

well to finish it... if you multiply a and c its 9 x 2 = 18

factors of 18 that add to 9... the coefficient of b are 6 and 3

so the next step is

(9x + 6)(9x + 3)
---------------   = 0
           9

remove the common factors from each binomial

3(3x + 2)3(3x + 1)
-------------------    = 0
              9

cancel the common factors  

and you get

(3x + 2)(3x + 1) = 0

this is a really effective method for dealing with any non-monic quadratic that can be factored.... it beats guess and check

perhaps you should show your teacher...

anonymous · Answer

Ok, I'll write it down!!! :)

campbell_st · Answer

tell you teacher it works every time

anonymous · Answer

I'll do that too

anonymous · Answer

I'm kind of torn on who to give the medal

anonymous · Answer

You both did a good job

anonymous · Answer

I chose DangerousJesse because I understood his explanation, but I don't know now