Question

solve using quadratic formula ; 2 n² - n - 45 = 0 plz explain step by step

Answer 1

Answer:

Step-by-step explanation:

Two solutions were found :

n = -9/2 = -4.500

n = 5

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (2n2 -  n) -  45  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  2n2-n-45  

The first term is,  2n2  its coefficient is  2 .

The middle term is,  -n  its coefficient is  -1 .

The last term, "the constant", is  -45  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -45 = -90  

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -1 .

     -90    +    1    =    -89  

     -45    +    2    =    -43  

     -30    +    3    =    -27  

     -18    +    5    =    -13  

     -15    +    6    =    -9  

     -10    +    9    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  9  

                    2n2 - 10n + 9n - 45

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2n • (n-5)

             Add up the last 2 terms, pulling out common factors :

                   9 • (n-5)

Step-5 : Add up the four terms of step 4 :

                   (2n+9)  •  (n-5)

            Which is the desired factorization

Answer 2

Answer:

Please find attachment.