SOLUTION: Solve [8/(t+5)]=[(t-3)/(t^2+7t+10)+(1/3). Round to the nearest hundredth. Thank You! :)

Question 1042452: Solve [8/(t+5)]=[(t-3)/(t^2+7t+10)+(1/3). Round to the nearest hundredth.
Thank You! :)

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
[8/(t+5)]=[(t-3)/(t^2+7t+10)+(1/3)
:
8 / (t+5) = (t-3)/(t+5)(t+2) + (1/3)
:
the common denominator is (t+5)(t+2)3
:
multiply both sides of = by common denominator
:
(8)(3)(t+2) = 3(t-3) + (t+5)(t+2)
:
24t +48 = 3t-9 + t^2+7t+10
:
t^2 -14t = 47
:
complete the square
:
t^2 -14t +49 = 47 + 49
:
(t - 7)^2 = 96
:
t - 7 = + or - 9.798
:
***********************************
t = 7 + 9.798 = 16.798 approx 16.80
t = 7 - 9.798 = -2.798 approx -2.80
***********************************
:
answers are checked by substituting for t in original equation
:
for t = 16.80
0.367 = 0.3679
0.37 = 0.37
:
for t = -2.80
3.6364 = 3.6288
3.64 = 3.63
:
our answers checks

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