SOLUTION: Factor the quadratic. 2b(6b+13)=-12 I get 12b^2+26b+12=0 but not sure what to do next. May I please ask for assistance in solving this quadratic equation? Thanks

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Factor the quadratic. 2b(6b+13)=-12 I get 12b^2+26b+12=0 but not sure what to do next. May I please ask for assistance in solving this quadratic equation? Thanks       Log On


   

Question 246123: Factor the quadratic. 2b(6b+13)=-12
I get 12b^2+26b+12=0 but not sure what to do next. May I please ask for assistance in solving this quadratic equation? Thanks

Found 2 solutions by rapaljer, richwmiller:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct so far! Now you need to factor the left side. Start by taking out a common factor of 2:
12b^2 +26b+12=0
2(6b^2 +13b+6)=0

The trinomial needs to be factored. This is the hard part, which I call "Advanced Trinomial Factoring". You may want to see this lesson on my website, which I will explain later. For now, you can factor this into
2(3b+2)(2b+3)=0

The 2 does not affect the solutions at all. You have two solutions:
First,
3b+2=0
3b=-2
b=-2/3

Second,
2b+3=0
2b=-3
b=-3/2

For additional explanation on this topic, try my own website. Click on my tutor name "Rapaljer" anywhere in algebra.com. This takes you to my Homepage. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", then look in "Chapter 2" for "Section 2.09 Solving Quadratic Equations by Factoring." If your question was about this particular factoring, then look for my "Section 2.06 Advanced Trinomial Factoring."

My explanations are written for students who usually have trouble understanding math, and my own students say they can understand it a LOT easier than traditional textbooks. It is also supported by my "MATH IN LIVING COLOR" pages in which I solved the hardest problems IN COLOR! If you like my website, please recommend it to family and friends. It's all FREE!!

One more thought, if you had trouble with the factoring of this problem or any other problems with factoring, please see my FACTORING sections, which are near the beginning of this very same chapter. If you need help with factoring, I even have a free video of me teaching this lesson in my own classroom a few years ago. The video is also available FREE on my website!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
divide both sides by 12
12b^2+26b+12=0
you can solve by factoring, completng the square or by quadratic formula
You get -3/2 (-1.5) and -2/3 (-.667)
I like completing the square.
12b^2+26b=-12
divide by 12
b^2+(26/12)(b)=-1
b^2+(13/6)(b)=-1
add 1/2*(13/6)^2 =169/144 to both sides
b^2+(13/6)(b)+169/144=25/144
factor
|b+13/12|=-5/12
b=-5/12-13/12=-18/12=-3/2
b=+5/12-13/12=-8/12=-2/3
see below for other methods
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B26x%2B12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2826%29%5E2-4%2A12%2A12=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-26%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2826%29%2Bsqrt%28+100+%29%29%2F2%5C12+=+-0.666666666666667
x%5B2%5D+=+%28-%2826%29-sqrt%28+100+%29%29%2F2%5C12+=+-1.5

Quadratic expression 12x%5E2%2B26x%2B12 can be factored:
12x%5E2%2B26x%2B12+=+12%28x--0.666666666666667%29%2A%28x--1.5%29
Again, the answer is: -0.666666666666667, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B26%2Ax%2B12+%29