SOLUTION: 0=-16t^2+104t+56

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Question 580570: 0=-16t^2+104t+56
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
0=-16t%5E2%2B104t%2B56 Start with the given equation


-16t%5E2%2B104t%2B56=0 Flip the equation


16t%5E2-104t-56=0 Multiply every term by -1 to make the leading coefficient positive.



Notice that the quadratic 16t%5E2-104t-56 is in the form of At%5E2%2BBt%2BC where A=16, B=-104, and C=-56


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-%28-104%29+%2B-+sqrt%28+%28-104%29%5E2-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29 Plug in A=16, B=-104, and C=-56


t+=+%28104+%2B-+sqrt%28+%28-104%29%5E2-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29 Negate -104 to get 104.


t+=+%28104+%2B-+sqrt%28+10816-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29 Square -104 to get 10816.


t+=+%28104+%2B-+sqrt%28+10816--3584+%29%29%2F%282%2816%29%29 Multiply 4%2816%29%28-56%29 to get -3584


t+=+%28104+%2B-+sqrt%28+10816%2B3584+%29%29%2F%282%2816%29%29 Rewrite sqrt%2810816--3584%29 as sqrt%2810816%2B3584%29


t+=+%28104+%2B-+sqrt%28+14400+%29%29%2F%282%2816%29%29 Add 10816 to 3584 to get 14400


t+=+%28104+%2B-+sqrt%28+14400+%29%29%2F%2832%29 Multiply 2 and 16 to get 32.


t+=+%28104+%2B-+120%29%2F%2832%29 Take the square root of 14400 to get 120.


t+=+%28104+%2B+120%29%2F%2832%29 or t+=+%28104+-+120%29%2F%2832%29 Break up the expression.


t+=+%28224%29%2F%2832%29 or t+=++%28-16%29%2F%2832%29 Combine like terms.


t+=+7 or t+=+-1%2F2 Simplify.


So the solutions are t+=+7 or t+=+-1%2F2