SOLUTION: Please help me solve this equation: {{{ sqrt (sqrt (x+5) +x) = 5 }}}

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Question 996128: Please help me solve this equation: +sqrt+%28sqrt+%28x%2B5%29+%2Bx%29+=+5+
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The site stopped responding just after I submitted almost the entire solution process.

..
x^2-51x+620=0
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from quadratic equation, discriminant is 11%5E2.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
+sqrt+%28sqrt+%28x%2B5%29+%2Bx%29+ = +5+.

Square both sides. You will get

+sqrt+%28x%2B5%29+%2Bx+ = +25+.

sqrt%28x%2B5%29 = 25-x,

Square both sides again. You will get

x+%2B+5 = %2825+-+x%29%5E2,

x+%2B+5 = 625+-+50x+%2B+x%5E2,

x%5E2+-+51x+%2B+620 = 0.

x%5B1%5D = 20, x%5B2%5D = 31

Check. x%5B1%5D = 20 :   +sqrt+%28sqrt+%2820%2B5%29+%2B20%29+ = +sqrt+%28sqrt+%2825%29+%2B20%29+ = +sqrt+%285+%2B20%29+ = +sqrt+%2825%29+ = 5.         OK!

            x%5B2%5D = 31 :   +sqrt+%28sqrt+%2831%2B5%29+%2B31%29+ = +sqrt+%28sqrt+%2836%29+%2B31%29+ = +sqrt+%28-6+%2B31+%29+ = +sqrt+%2825%29+ = 5.     It is OK,  if you admit  sqrt%2836%29 = -6.