Question 722271: Could you please show me all steps to the factoring and solving? Also could you please show me how to check my solution back into the original equation?
For the Quadratic Formula problem, could you please include readable notation while you are working the computational steps?
Could you please show me the final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.
If possible and applicable, could you please show me how to incorporate the following four math vocabulary words into my steps?
-Quadratic formula
-Factoring
-Completing the square
-Discriminant
1. 2m^2 – m – 15 = 0
2. 2y^2 - 3y – 6 = 0
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
BEWARE: The Algebra.com system is cutting-off some of the expressions I am trying to write. Not my fault.!
A little bit of help on #1, but you must still study (your textbook) to make the best sense of it:
You can try to factor by using the format, (2m_______)(m________), and look for pairs of numbers which give the product of -15. Note, according to F.O.I.L. multiplication method, the O and I products must sum to -m.
What works? 15,1; 3,5; 5,3; 1,15?
The 5,3 combination seems to do something useful.
(2m_____5)(m_______3). Now you need to decide which operation in each binomial.
Skipping that and going to quadratic formula and discriminant:
Know that  is the discriminant for  . Applying discriminant for  , it will be  , POSITIVE 121. Read your book to know what this means. How many Real solutions?
Completing the Square allows you to change this general form equation, , into standard form. Standard form allows you to easily understand the graph of the equation. The part of the equation,  , represents a rectangle. The given equation does not really need completion of the square because it is found to be factorable to solve for m, but if you wished to have a graph or know more about the graph, then Completing the square may be very useful. You would first factor the 2 from the rectangular expression , and then ADD and SUBTRACT the square term, which is like a missing square piece obtained from examening the actual rectangle represented by  . If you would draw the picture, you will find that the term to use is  . I omit the rest of the process here. See and study your book.
 ,....
... will get you started.
|
|
|
