SOLUTION: y-(14/y) = 5 i got y^2-14=5y factored (y+7) (y-7)=5y y=0 help!

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Question 405271: y-(14/y) = 5
i got y^2-14=5y
factored (y+7) (y-7)=5y
y=0
help!
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're doing great until you come onto the step where you factor. So I'm going to start with the step before that one.



y%5E2-14=5y+ Start with the given equation.


y%5E2-5y-14=0+ Subtract 5y from both sides.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=1, b=-5, and c=-14


Let's use the quadratic formula to solve for y


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


y+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-5, and c=-14


y+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


y+=+%285+%2B-+sqrt%28+25-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


y+=+%285+%2B-+sqrt%28+25--56+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-14%29 to get -56


y+=+%285+%2B-+sqrt%28+25%2B56+%29%29%2F%282%281%29%29 Rewrite sqrt%2825--56%29 as sqrt%2825%2B56%29


y+=+%285+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 25 to 56 to get 81


y+=+%285+%2B-+sqrt%28+81+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%285+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


y+=+%285+%2B+9%29%2F%282%29 or y+=+%285+-+9%29%2F%282%29 Break up the expression.


y+=+%2814%29%2F%282%29 or y+=++%28-4%29%2F%282%29 Combine like terms.


y+=+7 or y+=+-2 Simplify.


So the answers are y+=+7 or y+=+-2


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y-%2814%2Fy%29+=+5...multiply by y

y%2Ay-%2814%2Fy%29y+=+5y

y%5E2-%2814%2Fcross%28y%29%29cross%28y%29+=+5y

y%5E2-14+=+5y

y%5E2-5y+-14+=+0........replace -5y with 2x-7y

y%5E2+%2B2y+-7y+-14+=+0.....Group the first two terms together and the last two terms together like this:

%28y%5E2+%2B2y%29+%2B%28-7y+-14%29+=+0

y%28y+%2B2%29+-7%28y%2B2%29+=+0......

%28y+-7%29%28y%2B2%29+=+0.