SOLUTION: Find the solution set for N. 6n^2 + 13n + 6 = 0 a. (2/3, 3/2) b. (2/3, -3/2) c. (-2/3, -3/2) d. (-2/3, 3/2)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the solution set for N. 6n^2 + 13n + 6 = 0 a. (2/3, 3/2) b. (2/3, -3/2) c. (-2/3, -3/2) d. (-2/3, 3/2)      Log On


   

Question 220175: Find the solution set for N.
6n^2 + 13n + 6 = 0
a. (2/3, 3/2)
b. (2/3, -3/2)
c. (-2/3, -3/2)
d. (-2/3, 3/2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for n:


Starting with the general quadratic


an%5E2%2Bbn%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve 6%2An%5E2%2B13%2An%2B6=0 ( notice a=6, b=13, and c=6)





n+=+%28-13+%2B-+sqrt%28+%2813%29%5E2-4%2A6%2A6+%29%29%2F%282%2A6%29 Plug in a=6, b=13, and c=6




n+=+%28-13+%2B-+sqrt%28+169-4%2A6%2A6+%29%29%2F%282%2A6%29 Square 13 to get 169




n+=+%28-13+%2B-+sqrt%28+169%2B-144+%29%29%2F%282%2A6%29 Multiply -4%2A6%2A6 to get -144




n+=+%28-13+%2B-+sqrt%28+25+%29%29%2F%282%2A6%29 Combine like terms in the radicand (everything under the square root)




n+=+%28-13+%2B-+5%29%2F%282%2A6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




n+=+%28-13+%2B-+5%29%2F12 Multiply 2 and 6 to get 12


So now the expression breaks down into two parts


n+=+%28-13+%2B+5%29%2F12 or n+=+%28-13+-+5%29%2F12


Lets look at the first part:


x=%28-13+%2B+5%29%2F12


n=-8%2F12 Add the terms in the numerator

n=-2%2F3 Divide


So one answer is

n=-2%2F3




Now lets look at the second part:


x=%28-13+-+5%29%2F12


n=-18%2F12 Subtract the terms in the numerator

n=-3%2F2 Divide


So another answer is

n=-3%2F2


So our solutions are:

n=-2%2F3 or n=-3%2F2