SOLUTION: Tutor please help me with this question 8(1+1/2)^2 +22(1+1/t)+15=0 Thank you!

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Question 105574: Tutor please help me with this question
8(1+1/2)^2 +22(1+1/t)+15=0
Thank you!

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
8%281%2B1%2F2%29%5E2+%2B22%281%2B1%2Ft%29%2B15=0
.
Inside the first set of parentheses, add the 1+%2B+1%2F2 which is the same as 1+%2B+.5
to get 1.5. Then square that quantity to get 1.5%5E2+=+2.25. This reduces the
problem to:
.
8%2A2.25+%2B+22%281%2B+1%2Ft%29+%2B+15+=+0
.
Multiplying the 8 times 2.25 results in 18 and the problem then is simplified to:
.
18+%2B+22%281+%2B+1%2Ft%29+%2B+15+=+0
.
Next, multiply the 22 times each of the terms in the remaining set of parentheses. The
22 times the 1 is 22 and the 22 times the 1%2Ft is 22%2Ft. This makes the equation
become:
.
18+%2B+22+%2B+22%2Ft+%2B+15+=+0
.
Then combine the 18 with the +22 and the +15 to get the sum 55. The equation is then:
.
55+%2B+22%2Ft+=+0
.
By subtracting 55 from both sides you separate the two terms and make the equation:
.
22%2Ft+=+-55
.
Multiply both sides of this equation by t to eliminate the denominator and make the equation:
.
22+=+-55t
.
Solve for t by dividing both sides by -55 and you have:
.
t+=+22%2F%28-55%29
.
Notice that both the numerator and the denominator have a common factor of 11. So you can
simplify the answer by dividing both by 11 to get:
.
t+=+2%2F%28-5%29+=+-2%2F5
.
Hope this helps you to understand the problem.