SOLUTION: 2x^2-7x-20

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Question 398880: 2x^2-7x-20
Found 2 solutions by MathLover1, rapaljer:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-7x-20
use quadratic formula

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ax%5E2-7%2Ax-20=0 ( notice a=2, b=-7, and c=-20)





x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A2%2A-20+%29%29%2F%282%2A2%29 Plug in a=2, b=-7, and c=-20




x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A2%2A-20+%29%29%2F%282%2A2%29 Negate -7 to get 7




x+=+%287+%2B-+sqrt%28+49-4%2A2%2A-20+%29%29%2F%282%2A2%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)




x+=+%287+%2B-+sqrt%28+49%2B160+%29%29%2F%282%2A2%29 Multiply -4%2A-20%2A2 to get 160




x+=+%287+%2B-+sqrt%28+209+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%287+%2B-+sqrt%28209%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%287+%2B-+sqrt%28209%29%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%287+%2B+sqrt%28209%29%29%2F4 or x+=+%287+-+sqrt%28209%29%29%2F4



Now break up the fraction



x=%2B7%2F4%2Bsqrt%28209%29%2F4 or x=%2B7%2F4-sqrt%28209%29%2F4



Simplify



x=7%2F4%2Bsqrt%28209%29%2F4 or x=7%2F4-sqrt%28209%29%2F4



So the solutions are:

x=7%2F4%2Bsqrt%28209%29%2F4 or x=7%2F4-sqrt%28209%29%2F4

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This is a FACTORING problem! In fact, because it starts off with a 2x^2 term, I call this one "Advanced Trinomial Factoring," and I have an entire section explaining this topic on my own website. I'll mention that later. First, let's solve the problem!!

2x^2 -7x - 20

This is a trinomial so we hope it factors into the product of two binomials. The First times First has to give you 2x^2, so it has to look like this:
(2x______)(x_______)

Next, the Last times Last has to give you a product of -20. Because the -20 is NEGATIVE, the signs within the binomials must be OPPOSITE. Moreover, because the middle term is an ODD number, it CANNOT be an EVEN number times an EVEN number. I think the most likely product to give you 20 is 5 times 4. There are two ways to write the 5*4 . If this doesn't work we'll try some other combinations to find the one that works.

(2x___5)(x____4) or (2x___4)(x___5)

Now, the middle term is -7x. You have to calculate the OUTER TIMES OUTER and the INNER TIMES INNER so the DIFFERENCE of these terms is -7x. In the first case above

(2x___5)(x____4)

the outer times outer is 2x*4=8x and the inner times inner is 5x. Since the difference here is NOT -7x, I conclude that this is NOT a possible factoring of this one.

Now, after trying the other possibilities on separate paper, I concluded that this does NOT factor. I also used a technique from higher math called calculating b^2-4ac, and I further concluded that this does NOT factor. Perhaps you miscopied the problem, or perhaps someone is playing what I consider a cruel trick on you by giving you a problem like this that is actually PRIME!!! As a teacher/author, I would NOT have done this to you.

The final answer is PRIME!!

For more information on my "Advanced Trinomial Factoring" please do visit my website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 2" for several topics on Factoring. Of course, you need to see the one called "Advanced Trinomial Factoring." Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

Check also for my VIDEO on factoring that was made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Basic Algebra" and look for the topic on "Factoring." If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

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