SOLUTION: How do you work this problem: The square route of x+10 plus the square route of x-6 equals 8.

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Question 70686: How do you work this problem: The square route of x+10 plus the square route of x-6 equals 8.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The square root of x+10 plus the square root of x-6 equals 8.
:
sqrt(x+10) + sqrt(x-6) = 8
:
Subtract sqrt(x-6) from both sides:
sqrt(x+10) = 8 - sqrt(x-6)
:
Square both sides, you have to FOIL (8 - sqrt(x-6)) * (8 - sqrt(x-6))
:
x + 10 = 64 - 8*sqrt(x-6) - 8*sqrt(x-6) + (x-6)
x + 10 = 64 - 16*sqrt(x-6) + (x-6)
x + 10 = 64 - 6 - 16*sqrt(x-6) + x
x + 10 = 58 - 16*sqrt(x-6) + x
x - x + 10 - 58 = -16*sqrt(x-6)
-48 = -16*sqrt(x-6)
:
Square both sides:
2304 = 256(x-6)
2304 = 256x - 1536
:
256x = 2304 + 1536
256x = 3840
x = 3840/256
x = 15
:
: substitute 15 for x in the original equation:
sqrt(15 + 10) + sqrt(15 - 6) = 8; proves our solution