Question

12x+13x=14
I'm asked to solve by completing the square (but we can solve the best/easiest way).
First I multiply both sides by 1/12 so the coefficient of x = 1. I am getting confused when I divide the second term by two and square.
13/12x becomes 13/24^2 becomes 169/576. Just doesn't look right to me... any thoughts?

Answer 1

Well, I think you're over-complicating it! :D
I would combine the like terms, 12x & 13x.
So then, you have 25x=14.
Divide each side by 25, and you get 0.56 or 14/25.

Answer 2

oh, my bad. that first term is 12x^2 :)

Answer 3

Oh, okay! So, you want the right side to equal to 0, so subtract 14 from both sides. That would give you
\[12^2 + 13x - 14 = 0\]
Factor it.
\[(-7 -4x)(2 -3x) = 0\]
So, in order for the equation to come out to be 0, one of the binomials needs to equal 0, right? So either (-7-4x) equals 0, or (2-3x) equals 0.
Let's solve the first one.
-7-4x = 0
Add 7 to both sides.
-4x = 7
Then, divide each side by -4.
7/ -4 is -1.75
Now we have our first answer. Let's go back to the second binomial, and solve it.
2-3x = 0
Subtract 2 from both sides.
-3x = -2
Divide each side by -3.
-2/-3 is about 0.67.

So x is equal to either -1.75 OR 0.67. Does that make sense?

Answer 4

I don't see from which stage you started factoring, from the original equation:
12x^2+13x-14=0
or from the point after I multiplied by 12/1 to clear the coefficient of x^2:
x^2+13/12x-14/12=0

Answer 5

(by the way, my name is Dana as well) :D

Answer 6

I started factoring from the original equation\[12x^2+13x-14=0\]

You have a fantastic name :D

Answer 7

I get it now :) For some reason my brain starts to have buffer overflow errors when I try to factor coefficients of x^ when it's not prime :) Thank you!

Answer 8

You're welcome! Glad I could help :D