SOLUTION: What value of x will satisfy this equation {{{sqrt(2x)+4=x}}}

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Question 1042927: What value of x will satisfy this equation
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
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What value of x will satisfy this equation
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Answer. x = 8.

Solution 

 =   --->   =   --->  square both sides --->

2x =   --->  2x =   --->   =   --->  factor left side --->

(x-2)*(x-8) = 0.

The roots are x = 2 and x = 8.

The root x = 8 satisfies the original equation.

The root x = 2 does not satisfy the original equation. It is an extraneous solution.


Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!



Subtract 4 from both sides





Square both sides to undo the square root

















or


or


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The two possible solutions are or


Let's check





Replace every x with 8








Possible solution is confirmed. So is a true solution


---------------------


Let's check





Replace every x with 2








This is false, so is extraneous. It is NOT a true solution.


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Final Answer:


is the only true solution to the original equation.
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