Question 143102
{{{sqrt(x)+4=sqrt(x+16)}}}  Start with the given equation



{{{(sqrt(x)+4)^2=x+16}}} Square both sides to eliminate the square root on the right side



{{{x+8*sqrt(x)+16=x+16}}} Foil the left side



{{{8*sqrt(x)=x+16-x-16}}}  Subtract x from both sides. Subtract 16 from both sides. 



{{{8*sqrt(x)=0}}} Combine like terms



{{{sqrt(x)=0}}} Divide both sides by 8



{{{x=0^2}}} Square both sides



{{{x=0}}} Simplify



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Answer:

So the solution is {{{x=0}}}