Expert: Paul Klarreich - 3/19/2008

Question
Hi.  I am resending the question with more information.  Can you tell me if I am doing this correctly?
Factor the following equation:
7x^2 + 23x + 6 = 0
Here is what I have so far:
first term
7x   1x
1x   7x
last term
2   3   1   6   
3   2   6   1
The set of terms that produce the middle term is
7x   2
1x   3
21x + 2 = 23x
Therefore, 7x^2 + 23x + 6 = 0 = (7x + 2)(1x + 3)
7x + 2 = 0     or     1x + 3 = 0
x = -2/7               x = -3/1

I am studying "quadratic equations" and "factoring ax^2 + bx + c"


Answer
Questioner:   Heather
Category:  Advanced Math
Private:  No
 
Subject:  equations
Question:  Hi.  I am resending the question with more information.  Can you tell me if I am doing this correctly?
Factor the following equation:
7x^2 + 23x + 6 = 0
Here is what I have so far:
first term
7x 1x
1x 7x
last term
2 3 1 6
3 2 6 1
The set of terms that produce the middle term is
7x 2
1x 3
21x + 2 = 23x
Therefore, 7x^2 + 23x + 6 = 0 = (7x + 2)(1x + 3)
7x + 2 = 0     or     1x + 3 = 0
x = -2/7               x = -3/1

I am studying "quadratic equations" and "factoring ax^2 + bx + c"
.........................................
Hi, Heather,

You did great!  
Of course there is no need to be writing x = -3/1; it's x = -3.
But everything else is fine.

Next week you learn to solve equations that cannot be factored.  Alas, in the real world that is true of most of them.  But the process will be fairly routine. Not to say you can't make some mistakes doing it, but I'll have some ideas for you then.

I look forward to hearing from you.