SOLUTION: Can someone please help me out with this. Thanks in advance t(9+t)=4(2t+5)

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Question 315590: Can someone please help me out with this. Thanks in advance
t(9+t)=4(2t+5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
t%289%2Bt%29=4%282t%2B5%29 Start with the given equation.


9t%2Bt%5E2=8t%2B20 Distribute.


9t%2Bt%5E2-8t-20=0 Get every term to the left side.


t%5E2%2Bt-20=0 Combine like terms.


Notice that the quadratic t%5E2%2Bt-20 is in the form of At%5E2%2BBt%2BC where A=1, B=1, and C=-20


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Plug in A=1, B=1, and C=-20


t+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


t+=+%28-1+%2B-+sqrt%28+1--80+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-20%29 to get -80


t+=+%28-1+%2B-+sqrt%28+1%2B80+%29%29%2F%282%281%29%29 Rewrite sqrt%281--80%29 as sqrt%281%2B80%29


t+=+%28-1+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 1 to 80 to get 81


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


t+=+%28-1+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


t+=+%28-1+%2B+9%29%2F%282%29 or t+=+%28-1+-+9%29%2F%282%29 Break up the expression.


t+=+%288%29%2F%282%29 or t+=++%28-10%29%2F%282%29 Combine like terms.


t+=+4 or t+=+-5 Simplify.


So the solutions are t+=+4 or t+=+-5