solve using quadratic formula ; 2 n² - n - 45 = 0 plz explain step by step
Answers
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:
Please find attachment.
