Question 768973
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sqrt(2x) + x = 4
sqrt(2x) + x - x = 4 - x
sqrt(2x) = 4 - x
(sqrt(2x))^2 = (4 - x)^2
2x = 16-4x-4x+x *[tex \LARGE \ \ \Leftarrow] Your problem is in this step.     
2x = 16-8x+x
2x = 16-7x
16-9x
-16/9 = x?


Should be:


*[tex \LARGE 2x\ =\ 16\ -\ 4x\ -\ 4x\ +\ x^2]


Collect like terms:


*[tex \LARGE x^2\ -\ 10x\ +\ 16\ =\ 0]


From here, factor and solve.  Then check both roots and discard any that do not create a true statement when substituted back into the original equation, since it is possible to introduce extraneous roots when you square both sides of an equation.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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