SOLUTION: 81t^2 = 49

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Question 237433: 81t^2 = 49
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

81t%5E2=49 Start with the given equation.


81t%5E2-49=0 Subtract 49 from both sides.


Notice that the quadratic 81t%5E2-49 is in the form of At%5E2%2BBt%2BC where A=81, B=0, and C=-49


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+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2881%29%28-49%29+%29%29%2F%282%2881%29%29 Plug in A=81, B=0, and C=-49


t+=+%280+%2B-+sqrt%28+0-4%2881%29%28-49%29+%29%29%2F%282%2881%29%29 Square 0 to get 0.


t+=+%280+%2B-+sqrt%28+0--15876+%29%29%2F%282%2881%29%29 Multiply 4%2881%29%28-49%29 to get -15876


t+=+%280+%2B-+sqrt%28+0%2B15876+%29%29%2F%282%2881%29%29 Rewrite sqrt%280--15876%29 as sqrt%280%2B15876%29


t+=+%280+%2B-+sqrt%28+15876+%29%29%2F%282%2881%29%29 Add 0 to 15876 to get 15876


t+=+%280+%2B-+sqrt%28+15876+%29%29%2F%28162%29 Multiply 2 and 81 to get 162.


t+=+%280+%2B-+126%29%2F%28162%29 Take the square root of 15876 to get 126.


t+=+%280+%2B+126%29%2F%28162%29 or t+=+%28-0+-+126%29%2F%28162%29 Break up the expression.


t+=+%28126%29%2F%28162%29 or t+=++%28-126%29%2F%28162%29 Combine like terms.


t+=+7%2F9 or t+=+-7%2F9 Simplify.


So the solutions are t+=+7%2F9 or t+=+-7%2F9