SOLUTION: t(t-1)=812 What are the steps to solve this equation?

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Question 226503: t(t-1)=812
What are the steps to solve this equation?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
t%28t-1%29=812 Start with the given equation.


t%5E2-t=812 Distribute.


t%5E2-t-812=0 Subtract 812 from both sides.


Notice we have a quadratic equation in the form of at%5E2%2Bbt%2Bc where a=1, b=-1, and c=-812


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%281%29%28-812%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=-812


t+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-812%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


t+=+%281+%2B-+sqrt%28+1-4%281%29%28-812%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


t+=+%281+%2B-+sqrt%28+1--3248+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-812%29 to get -3248


t+=+%281+%2B-+sqrt%28+1%2B3248+%29%29%2F%282%281%29%29 Rewrite sqrt%281--3248%29 as sqrt%281%2B3248%29


t+=+%281+%2B-+sqrt%28+3249+%29%29%2F%282%281%29%29 Add 1 to 3248 to get 3249


t+=+%281+%2B-+sqrt%28+3249+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


t+=+%281+%2B-+57%29%2F%282%29 Take the square root of 3249 to get 57.


t+=+%281+%2B+57%29%2F%282%29 or t+=+%281+-+57%29%2F%282%29 Break up the expression.


t+=+%2858%29%2F%282%29 or t+=++%28-56%29%2F%282%29 Combine like terms.


t+=+29 or t+=+-28 Simplify.


So the answers are t+=+29 or t+=+-28