SOLUTION: 7-1/t=6/t^2

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Question 146499: 7-1/t=6/t^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7-1%2Ft=6%2Ft%5E2 Start with the given equation.


t%5E2%287%29-t%5Ecross%282%29%281%2Fcross%28t%29%29=t%5E2%286%2Fcross%28t%5E2%29%29 Multiply every term by the LCD t%5E2

7t%5E2-t=6 Multiply and simplify.



7t%5E2-t-6=0 Subtract 6 from both sides.


Notice we have a quadratic equation in the form of at%5E2%2Bbt%2Bc where a=7, b=-1, and c=-6


Let's use the quadratic formula to solve for t


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


t+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%287%29%28-6%29+%29%29%2F%282%287%29%29 Plug in a=7, b=-1, and c=-6


t+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%287%29%28-6%29+%29%29%2F%282%287%29%29 Negate -1 to get 1.


t+=+%281+%2B-+sqrt%28+1-4%287%29%28-6%29+%29%29%2F%282%287%29%29 Square -1 to get 1.


t+=+%281+%2B-+sqrt%28+1--168+%29%29%2F%282%287%29%29 Multiply 4%287%29%28-6%29 to get -168


t+=+%281+%2B-+sqrt%28+1%2B168+%29%29%2F%282%287%29%29 Rewrite sqrt%281--168%29 as sqrt%281%2B168%29


t+=+%281+%2B-+sqrt%28+169+%29%29%2F%282%287%29%29 Add 1 to 168 to get 169


t+=+%281+%2B-+sqrt%28+169+%29%29%2F%2814%29 Multiply 2 and 7 to get 14.


t+=+%281+%2B-+13%29%2F%2814%29 Take the square root of 169 to get 13.


t+=+%281+%2B+13%29%2F%2814%29 or t+=+%281+-+13%29%2F%2814%29 Break up the expression.


t+=+%2814%29%2F%2814%29 or t+=++%28-12%29%2F%2814%29 Combine like terms.


t+=+1 or t+=+-6%2F7 Simplify.


So our answers are t+=+1 or t+=+-6%2F7