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20 = 32t - 16t2 Solve for t.  Please show how you got to your answer. If the answer is a non-real answer, show what the inaginary number will be.

 Mar 20, 2016
 #1
avatar+33616 
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One way is as follows:

 

roots

.

 Mar 20, 2016
edited by Alan  Mar 20, 2016
 #2
avatar+33616 
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My second line above should, of course, say "Divide through by 4 and rearrange"

.

 Mar 20, 2016
 #3
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20 = 32 t-16 t^2, solve for t:

20 = 32 t-16 t^2 is equivalent to 32 t-16 t^2 = 20:
32 t-16 t^2 = 20

Divide both sides by -16:
t^2-2 t = -5/4

Add 1 to both sides:
t^2-2 t+1 = -1/4

Write the left hand side as a square:
(t-1)^2 = -1/4

Take the square root of both sides:
t-1 = i/2 or t-1 = -i/2

Add 1 to both sides:
t = 1+i/2 or t-1 = -i/2

Add 1 to both sides:
Answer: |  t = 1+i/2       or       t = 1-i/2

 Mar 20, 2016

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