Question 380272: Solve equation by factoring: 24d^2 + 30d + 9 =0
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first step in any factoring problem is to take out the common factor, which in this case is 3.
3(8d^2+10d+3)=0
Next, you need to factor the trinomial. Because you have a coefficient of d^2 term greater than 1, I call this "Advanced Trinomial Factoring." Several methods are used by different people here, but I like the trial and error method. Start out by factoring the 8d^2 into either 4d*2d or 8d*d, probably 4d*2d:
3(4d+_____)(2d+_____)
Next, the blank spaces above must be filled in such that the product of the numbers is 3, probably 3*1 or 1*3, and ALSO, so that the middle term in the product of binomials will be 10d.
It DOES work!!! You are EXACTLY RIGHT!
3(4d+3)(2d+1)=0
There are two solutions:
First solution:
4d+3=0
4d=-3
d=-4/3
Second Solution:
2d+1=0
2d=-1
d=-1/2
For additional help with all kinds of WORD PROBLEMS, especially Perimeter problems, please see my own website. Just click on my tutor name "rapaljer" anywhere in algebra.com. A link there will connect you to my website. On my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 2" for the topics on FACTORING, and SOLVING QUADRATIC EQUATIONS. See also the solutions to many of these problems on my "MATH IN LIVING COLOR" pages that corrspond to these pages. Most people tell me that my explanations are a lot easier to understand than their expensive textbooks--and MINE ARE ALL FREE!!! Imgaine that!! If you like my explanations, all I ask is that you recommend them to friends and family!!
I also have videos on FACTORING from my own classes before I retired. From my Homepage, look for "Rapalje Videos in Living Color." Look in either Basic Algebra or Intermediate Algebra. The videos are also FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Dr. Rapalje
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