SOLUTION: Could you please show me the steps to factoring and solving the problem below? Also, could you please show me how to check my solution back into the original equation? Coul

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Could you please show me the steps to factoring and solving the problem below? Also, could you please show me how to check my solution back into the original equation? Coul      Log On


   

Question 722631: Could you please show me the steps to factoring and solving the problem below?
Also, could you please show me how to check my solution back into the original equation?
Could you please show me the final solutions as decimal approximations carried out to the third decimal place.
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
Found 2 solutions by lynnlo, mananth:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
PROBLEM: 2m^2-m-15=0
(1)FIND COEFFICIENTS A,B,C
A=2,B=-1,C=-15===============================QUADRATIC FORMULA
(2)PLUG IN YOUR VALUES FOR A,B,C INTO QUADRATIC FORMULA
x1,2,=-b±√b^2-4ac/2a
-(-1)±√(-1)^2-4*2*(-15)/2*2===FACTORING
(3)SIMPLIFY EXPRESSION UNDER SQUARE ROOT
X1,2,=1±√121/4==========DISCRIMINANT(121)
X1=1+√121/4=3
X2=1-√/4=-5/2
SOLUTION
-5/2,3

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2m%5E2-m-15
factoring
coefficient of middle term is -1
the product of first term and third term is 30
find two factors of 30 such that when you add them you get -1
Obviously they are -6and +5
2m%5E2-6m%2B5m-15=0

2m%28m-3%29%2B5%28m-3%29=0
%282m%2B5%29%28m-3%29=0
either 2m+5 =0 OR m-3=0 for the equation to be true
if 2m+5 = 0
then 2m=-5
m=-5/2
if m-3 =0
then m=3
so m=-5/2 or 3
completing the squares method
2m%5E2-m-15=0
the first term co efficient has to be 1
divide by 2
m%5E2-%28m%2F2%29+-%2815%2F2%29=0
m%5E2-%28m%2F2%29+=%2815%2F2%29
find the third term on the left side so that it is a perfect square
third term = (1/2 * co-efficient of second term)^2
=(1/2*1/2)^2
= 1/16
m%5E2-%28m%2F2%29+=%2815%2F2%29
add the third term to both sides
m%5E2-%28m%2F2%29%2B%281%2F16%29+=%2815%2F2%29%2B%281%2F16%29
%28m-%281%2F4%29%29%5E2=+-121%2F16
take the square root
m-(1/4) = +/- 11/4
so m= 3 or -
5/2