SOLUTION: square root 2x + 5 + square root x + 2 = 5

Question 971753: square root 2x + 5 + square root x + 2 = 5

Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sqrt (2x+5)=5-sqrt (x+2)
square both sides
2x +5 = 25 -10 sqrt (x+2) +x +2
collect terms
x+10 sqrt (x+2)=22
10 sqrt (x+2)=22-x
square both sides
100 (x+2)=484 -44x +x^2
100x +200=484-44x + x^2
x^2-144x+284=0
By quadratic formula sqrt (b^2-4ac)=140
x=(1/2) [144 +/-140]
x=142
x=2
Test solutions
sqrt 9 + sqrt 4=5 yes
sqrt 289 + sqrt 144=5 NO extraneous root
x=2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
square root 2x + 5 + square root x + 2 = 5
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Square both sides to get:
(2x+5) + 2sqrt[(2x+5)(x+2)] + (x+2) = 25
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2sqrt[(2x^2+9x+10)] = -3x+18
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Square both sides to get:
4[2x^2+9x+10] = (-3x+18)^2
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8x^2 + 36x+40 = 9x^2 - 108x + 324
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x^2 - 144x + 284 = 0
Factor::
(x-142)(x-2) = 0
---
Check those potential "answers" in the original equation::
Answer:: x = 2
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Cheers,
Stan H.
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