SOLUTION: sqrt(26t+10)-5sqrt(t)=1

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Question 164762: sqrt(26t+10)-5sqrt(t)=1
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(26t+10)-5sqrt(t)=1
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I'll assume you want to solve for t, tho you should say that.
sqrt%2826t%2B10%29-5sqrt%28t%29=1
sqrt%2826t%2B10%29=5sqrt%28t%29%2B1 Isolate one radical
Square both sides.
26t%2B10+=+25t+%2B+10sqrt%28t%29+%2B+1
Collect terms
t%2B9+=+10sqrt%28t%29
Square again
t%5E2+%2B+18t+%2B+81+=+100t
t%5E2+-+82t+%2B+81+=+0
(t-1)*(t-81) = 0
t = 1
t = 81
Check:
sqrt(26t+10)-5sqrt(t)=1
sqrt(26*1+10)-5sqrt(1)=1
sqrt(36)-5*1=1
6-5=1, so that one's good.
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sqrt%2826t%2B10%29-5sqrt%28t%29=1
sqrt%2826%2A81%2B10%29-5sqrt%2881%29=1
sqrt%282116%29-5sqrt%2881%29=1
46- 5*9 =1
46-45 = 1
That's good too.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2826t%2B10%29+-+5sqrt%28t%29 = 1
;
Add 5sqrt%28t%29 to both sides:
sqrt%2826t%2B10%29 = 1+%2B+5sqrt%28t%29
:
Square both sides (FOIL the right side)
26t + 10 = 1 + 10sqrt%28t%29 + 25t
:
Isolate the radical on the right
26t - 25t + 10 - 1 = 10sqrt%28t%29
:
t + 9 = 10sqrt%28t%29
:
Square both sides (FOIL the left)
t^2 + 18t + 81 = 100t
:
Arrange as a quadratic equation:
t^2 + 18t - 100t + 81 = 0
:
t^2 - 82t + 81 = 0
Factors to:
(t-81)(t-1) = 0
Two solutions
t = 81, and t = 1
:
Both solution should be checked in the original equation:
t=81
sqrt%2826%2881%29%2B10%29+-+5sqrt%2881%29 = 1
sqrt%282106%2B10%29 - 5 * 9 = 1
sqrt%282116%29 - 45 = 1
46 - 45 = 1; a good solution
;
You can check x=1 solution