SOLUTION: 5n^2-7n+2=0

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Question 419345: 5n^2-7n+2=0
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5n%5E2-7n%2B2=0 Start with the given equation.


Notice we have a quadratic equation in the form of an%5E2%2Bbn%2Bc where a=5, b=-7, and c=2


Let's use the quadratic formula to solve for n


n+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


n+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%285%29%282%29+%29%29%2F%282%285%29%29 Plug in a=5, b=-7, and c=2


n+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%285%29%282%29+%29%29%2F%282%285%29%29 Negate -7 to get 7.


n+=+%287+%2B-+sqrt%28+49-4%285%29%282%29+%29%29%2F%282%285%29%29 Square -7 to get 49.


n+=+%287+%2B-+sqrt%28+49-40+%29%29%2F%282%285%29%29 Multiply 4%285%29%282%29 to get 40


n+=+%287+%2B-+sqrt%28+9+%29%29%2F%282%285%29%29 Subtract 40 from 49 to get 9


n+=+%287+%2B-+sqrt%28+9+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


n+=+%287+%2B-+3%29%2F%2810%29 Take the square root of 9 to get 3.


n+=+%287+%2B+3%29%2F%2810%29 or n+=+%287+-+3%29%2F%2810%29 Break up the expression.


n+=+%2810%29%2F%2810%29 or n+=++%284%29%2F%2810%29 Combine like terms.


n+=+1 or n+=+2%2F5 Simplify.


So the answers are n+=+1 or n+=+2%2F5

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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

5n%5E2-7n%2B2=0.....factor...replace -7n with -5n-2n
5n%5E2-5n-2n%2B2=0...group first to and second two terms
%285n%5E2-5n%29-%282n-2%29=0
5n%28n-1%29-2%28n-1%29=0
%285n-2%29%28n-1%29=0
if 5n-2=0....->...n=2%2F5
if n-1=0....->...n=1

so, your solutions are:
n=2%2F5 or n=1